In[]:=
ClearAll["`*"];Remove["`*"];
In[]:=
sol=First@NDSolve[{y''[x]==y[x]Cos[x+y[x]],y[1]==1,y'[0]==1},y,{x,0,10}]
Out[]=
yInterpolatingFunction
Domain: {{0.,10.}}
Output: scalar

In[]:=
Plot[y[x]/.sol,{x,0,10}]
Out[]=
You can access the list of Properties of InterpolatingFunction object using:
In[]:=
PropertyList[y/.sol]
Out[]=
{Coordinates,DerivativeOrder,Domain,ElementMesh,Evaluate,GetPolynomial,Grid,IndexedElementEvaluate,InterpolationMethod,InterpolationOrder,MethodInformation,Methods,OutputDimensions,ParameterAddress,Periodicity,PlottableQ,Properties,QuantityUnits,Region,Unpack,ValuesOnGrid,VectorEvaluate}
In[]:=
{xmin,xmax}=(y/.sol[[1]])["Domain"][[1]];{xmin,xmax}
Out[]=
{0.,10.}
In[]:=
(y/.sol)["Coordinates"]
Out[]=
{{0.,0.000152675,0.00030535,0.00438901,0.00847268,0.0125563,0.0239532,0.0353501,0.0467471,0.058144,0.0785915,0.099039,0.119487,0.139934,0.160382,0.201277,0.242172,0.283067,0.323962,0.364857,0.405752,0.446647,0.487542,0.528437,0.569332,0.610228,0.651123,0.700745,0.750368,0.79999,0.849612,0.899235,0.948857,0.99848,1.0481,1.09772,1.14735,1.19697,1.24659,1.29621,1.34584,1.39546,1.44508,1.4947,1.54433,1.59395,1.64357,1.69319,1.74282,1.80005,1.85728,1.91451,1.9615,2.00849,2.05548,2.10247,2.14946,2.19645,2.24344,2.29883,2.35422,2.40961,2.465,2.52039,2.57578,2.63117,2.70958,2.78799,2.8664,2.94482,3.02323,3.10164,3.18006,3.2747,3.36934,3.46398,3.55863,3.65327,3.74791,3.84255,3.9372,4.03184,4.12648,4.22112,4.31577,4.41041,4.50505,4.5997,4.69434,4.69451,4.69467,4.69484,4.69501,4.69517,4.69551,4.69584,4.69618,4.69953,4.70287,4.70622,4.70957,4.74176,4.77395,4.80615,4.83834,4.87053,4.91566,4.96079,5.00592,5.05104,5.09617,5.1413,5.19427,5.24724,5.30021,5.35318,5.40615,5.45912,5.51209,5.56506,5.61803,5.671,5.73425,5.7975,5.86075,5.924,5.98725,6.0505,6.11375,6.177,6.24949,6.32199,6.39449,6.46698,6.53948,6.61198,6.68448,6.75697,6.82947,6.90197,6.97447,7.04696,7.11946,7.19196,7.28457,7.37719,7.4698,7.56242,7.65503,7.74764,7.84026,7.93287,8.02549,8.1181,8.19473,8.27136,8.33403,8.39669,8.45935,8.52202,8.58468,8.64735,8.71001,8.71012,8.71023,8.71035,8.71046,8.71057,8.7108,8.71102,8.71125,8.7135,8.71576,8.71801,8.72027,8.73611,8.75195,8.7678,8.78364,8.79948,8.82571,8.85194,8.87817,8.9044,8.93063,8.95685,8.98671,9.01656,9.04641,9.07626,9.10611,9.13596,9.16669,9.19742,9.22815,9.25888,9.28961,9.32033,9.35106,9.39,9.42893,9.46787,9.50681,9.54574,9.58468,9.62361,9.66255,9.70149,9.74042,9.77936,9.82311,9.86687,9.91062,9.95438,9.96331,9.97225,9.98118,9.99011,9.99506,10.}}
In[]:=
(y/.sol)["ValuesOnGrid"]
Out[]=
{-0.0641695,-0.0640168,-0.0638641,-0.059781,-0.055699,-0.0516178,-0.0402323,-0.028852,-0.0174755,-0.00610117,0.0143048,0.0347167,0.055143,0.0755919,0.0960718,0.137156,0.178456,0.220027,0.261921,0.304179,0.346835,0.389913,0.433428,0.47738,0.521758,0.566538,0.611681,0.666865,0.722379,0.778063,0.833732,0.889168,0.944129,0.998353,1.05156,1.10346,1.15376,1.20216,1.24839,1.29216,1.33323,1.37136,1.40635,1.43802,1.46624,1.49088,1.51185,1.5291,1.54261,1.55352,1.55945,1.56047,1.5577,1.55173,1.54263,1.53047,1.51534,1.4973,1.47645,1.44838,1.41665,1.3814,1.34279,1.30093,1.25597,1.20804,1.13535,1.05735,0.974382,0.886834,0.795082,0.69952,0.600561,0.477216,0.350374,0.220908,0.0897534,-0.0421002,-0.173614,-0.303715,-0.431307,-0.55529,-0.674578,-0.788117,-0.894899,-0.993983,-1.0845,-1.1657,-1.2369,-1.23702,-1.23714,-1.23725,-1.23737,-1.23749,-1.23772,-1.23795,-1.23818,-1.24051,-1.24281,-1.24511,-1.24739,-1.26865,-1.28867,-1.30744,-1.32493,-1.34114,-1.36171,-1.37973,-1.39521,-1.40816,-1.41859,-1.42654,-1.43276,-1.43571,-1.43551,-1.43229,-1.42621,-1.41746,-1.40624,-1.39277,-1.37729,-1.36005,-1.33755,-1.31338,-1.28802,-1.26195,-1.23562,-1.20948,-1.18396,-1.15946,-1.13311,-1.10909,-1.08787,-1.06984,-1.05537,-1.04477,-1.0383,-1.03622,-1.03874,-1.04608,-1.05842,-1.07595,-1.09886,-1.12735,-1.17219,-1.22694,-1.29214,-1.36836,-1.45627,-1.55664,-1.67032,-1.79823,-1.94141,-2.10091,-2.24597,-2.40349,-2.54187,-2.68904,-2.84506,-3.00982,-3.18305,-3.36419,-3.55245,-3.5528,-3.55314,-3.55349,-3.55383,-3.55418,-3.55486,-3.55555,-3.55624,-3.56314,-3.57004,-3.57696,-3.58388,-3.63271,-3.68189,-3.73139,-3.7812,-3.83127,-3.91469,-3.99863,-4.08297,-4.16753,-4.25217,-4.3367,-4.43257,-4.52781,-4.62216,-4.71533,-4.80706,-4.89707,-4.98765,-5.07583,-5.16135,-5.24393,-5.32334,-5.39933,-5.4717,-5.55788,-5.63758,-5.71047,-5.7763,-5.83485,-5.88595,-5.92949,-5.96537,-5.99358,-6.01413,-6.02707,-6.0327,-6.02913,-6.01672,-5.9959,-5.99067,-5.98511,-5.97924,-5.97305,-5.9695,-5.96585}
In[]:=
(y/.sol)["InterpolationMethod"]
Out[]=
Hermite
In[]:=
(y/.sol)["Region"]
Out[]=
In[]:=
(y/.sol)["PlottableQ"]
Out[]=
True
In[]:=
(*-----------------------------------------------------------------------------------------*)
In[]:=
Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"];
In[]:=
InterpolatingFunctionDomain[y/.sol]
Out[]=
{{0.,10.}}
In[]:=
InterpolatingFunctionCoordinates[y/.sol]
Out[]=
{{0.,0.000152675,0.00030535,0.00438901,0.00847268,0.0125563,0.0239532,0.0353501,0.0467471,0.058144,0.0785915,0.099039,0.119487,0.139934,0.160382,0.201277,0.242172,0.283067,0.323962,0.364857,0.405752,0.446647,0.487542,0.528437,0.569332,0.610228,0.651123,0.700745,0.750368,0.79999,0.849612,0.899235,0.948857,0.99848,1.0481,1.09772,1.14735,1.19697,1.24659,1.29621,1.34584,1.39546,1.44508,1.4947,1.54433,1.59395,1.64357,1.69319,1.74282,1.80005,1.85728,1.91451,1.9615,2.00849,2.05548,2.10247,2.14946,2.19645,2.24344,2.29883,2.35422,2.40961,2.465,2.52039,2.57578,2.63117,2.70958,2.78799,2.8664,2.94482,3.02323,3.10164,3.18006,3.2747,3.36934,3.46398,3.55863,3.65327,3.74791,3.84255,3.9372,4.03184,4.12648,4.22112,4.31577,4.41041,4.50505,4.5997,4.69434,4.69451,4.69467,4.69484,4.69501,4.69517,4.69551,4.69584,4.69618,4.69953,4.70287,4.70622,4.70957,4.74176,4.77395,4.80615,4.83834,4.87053,4.91566,4.96079,5.00592,5.05104,5.09617,5.1413,5.19427,5.24724,5.30021,5.35318,5.40615,5.45912,5.51209,5.56506,5.61803,5.671,5.73425,5.7975,5.86075,5.924,5.98725,6.0505,6.11375,6.177,6.24949,6.32199,6.39449,6.46698,6.53948,6.61198,6.68448,6.75697,6.82947,6.90197,6.97447,7.04696,7.11946,7.19196,7.28457,7.37719,7.4698,7.56242,7.65503,7.74764,7.84026,7.93287,8.02549,8.1181,8.19473,8.27136,8.33403,8.39669,8.45935,8.52202,8.58468,8.64735,8.71001,8.71012,8.71023,8.71035,8.71046,8.71057,8.7108,8.71102,8.71125,8.7135,8.71576,8.71801,8.72027,8.73611,8.75195,8.7678,8.78364,8.79948,8.82571,8.85194,8.87817,8.9044,8.93063,8.95685,8.98671,9.01656,9.04641,9.07626,9.10611,9.13596,9.16669,9.19742,9.22815,9.25888,9.28961,9.32033,9.35106,9.39,9.42893,9.46787,9.50681,9.54574,9.58468,9.62361,9.66255,9.70149,9.74042,9.77936,9.82311,9.86687,9.91062,9.95438,9.96331,9.97225,9.98118,9.99011,9.99506,10.}}
In[]:=
InterpolatingFunctionGrid[y/.sol]
Out[]=
{{0.},{0.000152675},{0.00030535},{0.00438901},{0.00847268},{0.0125563},{0.0239532},{0.0353501},{0.0467471},{0.058144},{0.0785915},{0.099039},{0.119487},{0.139934},{0.160382},{0.201277},{0.242172},{0.283067},{0.323962},{0.364857},{0.405752},{0.446647},{0.487542},{0.528437},{0.569332},{0.610228},{0.651123},{0.700745},{0.750368},{0.79999},{0.849612},{0.899235},{0.948857},{0.99848},{1.0481},{1.09772},{1.14735},{1.19697},{1.24659},{1.29621},{1.34584},{1.39546},{1.44508},{1.4947},{1.54433},{1.59395},{1.64357},{1.69319},{1.74282},{1.80005},{1.85728},{1.91451},{1.9615},{2.00849},{2.05548},{2.10247},{2.14946},{2.19645},{2.24344},{2.29883},{2.35422},{2.40961},{2.465},{2.52039},{2.57578},{2.63117},{2.70958},{2.78799},{2.8664},{2.94482},{3.02323},{3.10164},{3.18006},{3.2747},{3.36934},{3.46398},{3.55863},{3.65327},{3.74791},{3.84255},{3.9372},{4.03184},{4.12648},{4.22112},{4.31577},{4.41041},{4.50505},{4.5997},{4.69434},{4.69451},{4.69467},{4.69484},{4.69501},{4.69517},{4.69551},{4.69584},{4.69618},{4.69953},{4.70287},{4.70622},{4.70957},{4.74176},{4.77395},{4.80615},{4.83834},{4.87053},{4.91566},{4.96079},{5.00592},{5.05104},{5.09617},{5.1413},{5.19427},{5.24724},{5.30021},{5.35318},{5.40615},{5.45912},{5.51209},{5.56506},{5.61803},{5.671},{5.73425},{5.7975},{5.86075},{5.924},{5.98725},{6.0505},{6.11375},{6.177},{6.24949},{6.32199},{6.39449},{6.46698},{6.53948},{6.61198},{6.68448},{6.75697},{6.82947},{6.90197},{6.97447},{7.04696},{7.11946},{7.19196},{7.28457},{7.37719},{7.4698},{7.56242},{7.65503},{7.74764},{7.84026},{7.93287},{8.02549},{8.1181},{8.19473},{8.27136},{8.33403},{8.39669},{8.45935},{8.52202},{8.58468},{8.64735},{8.71001},{8.71012},{8.71023},{8.71035},{8.71046},{8.71057},{8.7108},{8.71102},{8.71125},{8.7135},{8.71576},{8.71801},{8.72027},{8.73611},{8.75195},{8.7678},{8.78364},{8.79948},{8.82571},{8.85194},{8.87817},{8.9044},{8.93063},{8.95685},{8.98671},{9.01656},{9.04641},{9.07626},{9.10611},{9.13596},{9.16669},{9.19742},{9.22815},{9.25888},{9.28961},{9.32033},{9.35106},{9.39},{9.42893},{9.46787},{9.50681},{9.54574},{9.58468},{9.62361},{9.66255},{9.70149},{9.74042},{9.77936},{9.82311},{9.86687},{9.91062},{9.95438},{9.96331},{9.97225},{9.98118},{9.99011},{9.99506},{10.}}
In[]:=
InterpolatingFunctionValuesOnGrid[y/.sol]
Out[]=
{-0.0641695,-0.0640168,-0.0638641,-0.059781,-0.055699,-0.0516178,-0.0402323,-0.028852,-0.0174755,-0.00610117,0.0143048,0.0347167,0.055143,0.0755919,0.0960718,0.137156,0.178456,0.220027,0.261921,0.304179,0.346835,0.389913,0.433428,0.47738,0.521758,0.566538,0.611681,0.666865,0.722379,0.778063,0.833732,0.889168,0.944129,0.998353,1.05156,1.10346,1.15376,1.20216,1.24839,1.29216,1.33323,1.37136,1.40635,1.43802,1.46624,1.49088,1.51185,1.5291,1.54261,1.55352,1.55945,1.56047,1.5577,1.55173,1.54263,1.53047,1.51534,1.4973,1.47645,1.44838,1.41665,1.3814,1.34279,1.30093,1.25597,1.20804,1.13535,1.05735,0.974382,0.886834,0.795082,0.69952,0.600561,0.477216,0.350374,0.220908,0.0897534,-0.0421002,-0.173614,-0.303715,-0.431307,-0.55529,-0.674578,-0.788117,-0.894899,-0.993983,-1.0845,-1.1657,-1.2369,-1.23702,-1.23714,-1.23725,-1.23737,-1.23749,-1.23772,-1.23795,-1.23818,-1.24051,-1.24281,-1.24511,-1.24739,-1.26865,-1.28867,-1.30744,-1.32493,-1.34114,-1.36171,-1.37973,-1.39521,-1.40816,-1.41859,-1.42654,-1.43276,-1.43571,-1.43551,-1.43229,-1.42621,-1.41746,-1.40624,-1.39277,-1.37729,-1.36005,-1.33755,-1.31338,-1.28802,-1.26195,-1.23562,-1.20948,-1.18396,-1.15946,-1.13311,-1.10909,-1.08787,-1.06984,-1.05537,-1.04477,-1.0383,-1.03622,-1.03874,-1.04608,-1.05842,-1.07595,-1.09886,-1.12735,-1.17219,-1.22694,-1.29214,-1.36836,-1.45627,-1.55664,-1.67032,-1.79823,-1.94141,-2.10091,-2.24597,-2.40349,-2.54187,-2.68904,-2.84506,-3.00982,-3.18305,-3.36419,-3.55245,-3.5528,-3.55314,-3.55349,-3.55383,-3.55418,-3.55486,-3.55555,-3.55624,-3.56314,-3.57004,-3.57696,-3.58388,-3.63271,-3.68189,-3.73139,-3.7812,-3.83127,-3.91469,-3.99863,-4.08297,-4.16753,-4.25217,-4.3367,-4.43257,-4.52781,-4.62216,-4.71533,-4.80706,-4.89707,-4.98765,-5.07583,-5.16135,-5.24393,-5.32334,-5.39933,-5.4717,-5.55788,-5.63758,-5.71047,-5.7763,-5.83485,-5.88595,-5.92949,-5.96537,-5.99358,-6.01413,-6.02707,-6.0327,-6.02913,-6.01672,-5.9959,-5.99067,-5.98511,-5.97924,-5.97305,-5.9695,-5.96585}
In[]:=
InterpolatingFunctionInterpolationOrder[y/.sol]
Out[]=
{3}
In[]:=
InterpolatingFunctionDerivativeOrder[y/.sol]
Out[]=
0
In[]:=
(*--------------------------------------------------------------------------------------*)
In[]:=
Print/@(y/.sol)/@{"Coordinates","DerivativeOrder","Domain","ElementMesh","Evaluate","Grid","InterpolationMethod","InterpolationOrder","Methods","OutputDimensions","Periodicity","PlottableQ","Properties","QuantityUnits","ValuesOnGrid"};
{{0.,0.000152675,0.00030535,0.00438901,0.00847268,0.0125563,0.0239532,0.0353501,0.0467471,0.058144,0.0785915,0.099039,0.119487,0.139934,0.160382,0.201277,0.242172,0.283067,0.323962,0.364857,0.405752,0.446647,0.487542,0.528437,0.569332,0.610228,0.651123,0.700745,0.750368,0.79999,0.849612,0.899235,0.948857,0.99848,1.0481,1.09772,1.14735,1.19697,1.24659,1.29621,1.34584,1.39546,1.44508,1.4947,1.54433,1.59395,1.64357,1.69319,1.74282,1.80005,1.85728,1.91451,1.9615,2.00849,2.05548,2.10247,2.14946,2.19645,2.24344,2.29883,2.35422,2.40961,2.465,2.52039,2.57578,2.63117,2.70958,2.78799,2.8664,2.94482,3.02323,3.10164,3.18006,3.2747,3.36934,3.46398,3.55863,3.65327,3.74791,3.84255,3.9372,4.03184,4.12648,4.22112,4.31577,4.41041,4.50505,4.5997,4.69434,4.69451,4.69467,4.69484,4.69501,4.69517,4.69551,4.69584,4.69618,4.69953,4.70287,4.70622,4.70957,4.74176,4.77395,4.80615,4.83834,4.87053,4.91566,4.96079,5.00592,5.05104,5.09617,5.1413,5.19427,5.24724,5.30021,5.35318,5.40615,5.45912,5.51209,5.56506,5.61803,5.671,5.73425,5.7975,5.86075,5.924,5.98725,6.0505,6.11375,6.177,6.24949,6.32199,6.39449,6.46698,6.53948,6.61198,6.68448,6.75697,6.82947,6.90197,6.97447,7.04696,7.11946,7.19196,7.28457,7.37719,7.4698,7.56242,7.65503,7.74764,7.84026,7.93287,8.02549,8.1181,8.19473,8.27136,8.33403,8.39669,8.45935,8.52202,8.58468,8.64735,8.71001,8.71012,8.71023,8.71035,8.71046,8.71057,8.7108,8.71102,8.71125,8.7135,8.71576,8.71801,8.72027,8.73611,8.75195,8.7678,8.78364,8.79948,8.82571,8.85194,8.87817,8.9044,8.93063,8.95685,8.98671,9.01656,9.04641,9.07626,9.10611,9.13596,9.16669,9.19742,9.22815,9.25888,9.28961,9.32033,9.35106,9.39,9.42893,9.46787,9.50681,9.54574,9.58468,9.62361,9.66255,9.70149,9.74042,9.77936,9.82311,9.86687,9.91062,9.95438,9.96331,9.97225,9.98118,9.99011,9.99506,10.}}