In[]:=
ClearAll["`*"];Remove["`*"];
Remove
:There are no symbols matching "`*.
In[]:=
$Version
Out[]=
14.0.0 for Microsoft Windows (64-bit) (December 13, 2023)
In[]:=
S=DSolveChangeVariablesDSolve[y'[x]==(7x+4y[x])/(7x+4y[x]+4),y,x],u,x,y[x]
(u[x]-7x)
4
//FullSimplify
Out[]=
DSolve
16
4+u[x]
+
′
u
[x]11,u,x
In[]:=
W=(S//Activate)
Solve
:Inverse functions are being used by Solve​, so some solutions may not be found; use Reduce for complete solution information.
Out[]=
uFunction{x},
4
11
-7+4ProductLog-
1
16
1/16
(
121x+121

1

)
,uFunction{x},
4
11
-7+4ProductLog-
1
16

1/16
(
121x+121

1

)
,uFunction{x},
4
11
-7+4ProductLog
1
16

1/16
(
121x+121

1

)
,uFunction{x},
4
11
-7+4ProductLog
1
16
1/16
(
121x+121

1

)
,uFunction{x},
4
11
-7+4ProductLog-
1
16
1/8
(-1)
1/16
(
121x+121

1

)
,uFunction{x},
4
11
-7+4ProductLog
1
16
1/8
(-1)
1/16
(
121x+121

1

)
,uFunction{x},
4
11
-7+4ProductLog-
1
16
1/4
(-1)
1/16
(
121x+121

1

)
,uFunction{x},
4
11
-7+4ProductLog
1
16
1/4
(-1)
1/16
(
121x+121

1

)
,uFunction{x},
4
11
-7+4ProductLog-
1
16
3/8
(-1)
1/16
(
121x+121

1

)
,uFunction{x},
4
11
-7+4ProductLog
1
16
3/8
(-1)
1/16
(
121x+121

1

)
,uFunction{x},
4
11
-7+4ProductLog-
1
16
5/8
(-1)
1/16
(
121x+121

1

)
,uFunction{x},
4
11
-7+4ProductLog
1
16
5/8
(-1)
1/16
(
121x+121

1

)
,uFunction{x},
4
11
-7+4ProductLog-
1
16
3/4
(-1)
1/16
(
121x+121

1

)
,uFunction{x},
4
11
-7+4ProductLog
1
16
3/4
(-1)
1/16
(
121x+121

1

)
,uFunction{x},
4
11
-7+4ProductLog-
1
16
7/8
(-1)
1/16
(
121x+121

1

)
,uFunction{x},
4
11
-7+4ProductLog
1
16
7/8
(-1)
1/16
(
121x+121

1

)

In[]:=
16
4+u[x]
+
′
u
[x]11/.W//FullSimplify
Out[]=
{True,True,True,True,True,True,True,True,True,True,True,True,True,True,True,True}
In[]:=
S1=DSolveChangeVariablesDSolve[{y'[x]==(7x+4y[x])/(7x+4y[x]+4),y[-1]==-1},y,x],u,x,y[x]
(u[x]-7x)
4
//FullSimplify
Out[]=
DSolve
16
4+u[x]
+
′
u
[x]11,11+u[-1]0,u,x
In[]:=
S1//Activate
Solve
:Inverse functions are being used by Solve​, so some solutions may not be found; use Reduce for complete solution information.
Solve
:Inverse functions are being used by Solve​, so some solutions may not be found; use Reduce for complete solution information.
Solve
:Inverse functions are being used by Solve​, so some solutions may not be found; use Reduce for complete solution information.
General
:Further output of Solve::ifun will be suppressed during this calculation.
DSolve
:For some branches of the general solution, the given boundary conditions lead to an empty solution.
DSolve
:For some branches of the general solution, the given boundary conditions lead to an empty solution.
DSolve
:For some branches of the general solution, the given boundary conditions lead to an empty solution.
General
:Further output of DSolve::bvnul will be suppressed during this calculation.
Out[]=
{}
In[]:=
S2=DSolveChangeVariablesDSolve[{y'[x]==(7x+4y[x])/(7x+4y[x]+4),y[a]==b},y,x],u,x,y[x]
(u[x]-7x)
4
//FullSimplify
Out[]=
DSolve
16
4+u[x]
+
′
u
[x]11,7a+4bu[a],u,x
In[]:=
S2//Activate
Solve
:Inverse functions are being used by Solve​, so some solutions may not be found; use Reduce for complete solution information.
Solve
:Inverse functions are being used by Solve​, so some solutions may not be found; use Reduce for complete solution information.
Solve
:Inverse functions are being used by Solve​, so some solutions may not be found; use Reduce for complete solution information.
General
:Further output of Solve::ifun will be suppressed during this calculation.
Out[]=
uFunction{x},
4
11
-7+4ProductLog-
1
16
1/16

16
(28+77a+44b)
28-44a+44b+121x


,uFunction{x},
4
11
-7+4ProductLog-
1
16

1/16

16
(28+77a+44b)
28-44a+44b+121x


,uFunction{x},
4
11
-7+4ProductLog
1
16

1/16

16
(28+77a+44b)
28-44a+44b+121x


,uFunction{x},
4
11
-7+4ProductLog
1
16
1/16

16
(28+77a+44b)
28-44a+44b+121x


,uFunction{x},
4
11
-7+4ProductLog-
1
16
1/8
(-1)
1/16

16
(28+77a+44b)
28-44a+44b+121x


,uFunction{x},
4
11
-7+4ProductLog
1
16
1/8
(-1)
1/16

16
(28+77a+44b)
28-44a+44b+121x


,uFunction{x},
4
11
-7+4ProductLog-
1
16
1/4
(-1)
1/16

16
(28+77a+44b)
28-44a+44b+121x


,uFunction{x},
4
11
-7+4ProductLog
1
16
1/4
(-1)
1/16

16
(28+77a+44b)
28-44a+44b+121x


,uFunction{x},
4
11
-7+4ProductLog-
1
16
3/8
(-1)
1/16

16
(28+77a+44b)
28-44a+44b+121x


,uFunction{x},
4
11
-7+4ProductLog
1
16
3/8
(-1)
1/16

16
(28+77a+44b)
28-44a+44b+121x


,uFunction{x},
4
11
-7+4ProductLog-
1
16
5/8
(-1)
1/16

16
(28+77a+44b)
28-44a+44b+121x


,uFunction{x},
4
11
-7+4ProductLog
1
16
5/8
(-1)
1/16

16
(28+77a+44b)
28-44a+44b+121x


,uFunction{x},
4
11
-7+4ProductLog-
1
16
3/4
(-1)
1/16

16
(28+77a+44b)
28-44a+44b+121x


,uFunction{x},
4
11
-7+4ProductLog
1
16
3/4
(-1)
1/16

16
(28+77a+44b)
28-44a+44b+121x


,uFunction{x},
4
11
-7+4ProductLog-
1
16
7/8
(-1)
1/16

16
(28+77a+44b)
28-44a+44b+121x


,uFunction{x},
4
11
-7+4ProductLog
1
16
7/8
(-1)
1/16

16
(28+77a+44b)
28-44a+44b+121x



In[]:=

16
4+u[x]
+
′
u
[x]11,7a+4bu[a]/.((S2//Activate))/.a->-1/.b->-1//FullSimplify
Solve
:Inverse functions are being used by Solve​, so some solutions may not be found; use Reduce for complete solution information.
Solve
:Inverse functions are being used by Solve​, so some solutions may not be found; use Reduce for complete solution information.
Solve
:Inverse functions are being used by Solve​, so some solutions may not be found; use Reduce for complete solution information.
General
:Further output of Solve::ifun will be suppressed during this calculation.
Out[]=
{{True,False},{True,False},{True,False},{True,False},{True,False},{True,False},{True,False},{True,False},{True,False},{True,False},{True,False},{True,False},{True,False},{True,False},{True,False},{True,False}}