Combustion Equation Chemical Equilibrium Differential Equations

Clear[x1,x2,x3,x4,x2K,x3K,dx1,dx2,dx3,dx4,dx2K,dx3K,dy1,dy2]​​​​x1=2(1-y1)/(2+y1(1+y2));​​​​x2=y1(1-y2)/(2+y1(1+y2));​​​​x3=2y1/(2+y1(1+y2));​​​​x4=(2y1*y2)/(2+y1(1+y2));​​​​"dx1"​​​​dx1=Collect[D[x1,y1]dy1+D[x1,y2]dy2,{dy1,dy2},Simplify]​​​​"dx2"​​​​dx2=Collect[D[x2,y1]dy1+D[x2,y2]dy2,{dy1,dy2},Simplify]​​​​"dx3"​​​​dx3=Collect[D[x3,y1]dy1+D[x3,y2]dy2,{dy1,dy2},Simplify]​​​​​​"dx4"​​​​dx4=Collect[D[x4,y1]dy1+D[x4,y2]dy2,{dy1,dy2},Simplify]​​​​x2K=(x4^2*P)/(K2^2);​​​​x3K=(x1^2)/(x2^2*K1^2*P);​​​​"dx2k"​​​​dx2K=Collect[D[x2K,y1]dy1+D[x2K,y2]dy2+D[x2K,P]dP+D[x2K,K2]dK2,{dy1,dy2},Simplify]​​​​"dx3k"​​​​dx3K=Collect[D[x3K,y1]dy1+D[x3K,y2]dy2+D[x3K,P]dP+D[x3K,K1]dK1,{dy1,dy2},Simplify]​​​​Solve[{dx2==dx2K,dx3==dx3K},{dy1,dy2}]​​​​FullSimplify[Solve[{Cm1*dy1+Cm2*dy2==Ck1*dy1+Ck2*dy2+Ck3,Cm3*dy1+Cm4*dy2==Ck4*dy1+Ck5*dy2+Ck6},{dy1,dy2}]]
Out[]=
dx1
Out[]=
2dy2(-1+y1)y1
2
(2+y1+y1y2)
-
2dy1(3+y2)
2
(2+y1+y1y2)
Out[]=
dx2
Out[]=
-
2dy2y1(1+y1)
2
(2+y1+y1y2)
-
2dy1(-1+y2)
2
(2+y1+y1y2)
Out[]=
dx3
Out[]=
4dy1
2
(2+y1+y1y2)
-
2dy2
2
y1
2
(2+y1+y1y2)
Out[]=
dx4
Out[]=
2dy2y1(2+y1)
2
(2+y1+y1y2)
+
4dy1y2
2
(2+y1+y1y2)
Out[]=
dx2k
Out[]=
8dy2P
2
y1
(2+y1)y2
2
K2
3
(2+y1+y1y2)
+
16dy1Py1
2
y2
2
K2
3
(2+y1+y1y2)
+
4(dPK2-2dK2P)
2
y1
2
y2
3
K2
2
(2+y1+y1y2)
Out[]=
dx3k
Out[]=
-
8dy2
2
(-1+y1)
2
K1
P
2
y1
3
(-1+y2)
+
8dy1(-1+y1)
2
K1
P
3
y1
2
(-1+y2)
-
4(dPK1+2dK1P)
2
(-1+y1)
3
K1
2
P
2
y1
2
(-1+y2)
Out[]=
Out[]=
dy1
Ck6(Ck2-Cm2)+Ck3(-Ck5+Cm4)
-((Ck2-Cm2)(Ck4-Cm3))+(Ck1-Cm1)(Ck5-Cm4)
,dy2
Ck6(-Ck1+Cm1)+Ck3(Ck4-Cm3)
-((Ck2-Cm2)(Ck4-Cm3))+(Ck1-Cm1)(Ck5-Cm4)
