I try to solve a system of six couple linear PDF. I applied the Laplace transform method and with some simplifications I retain with the following three coupled ODE
eq1=s^2*(1-w)*e[x] + C1*D[e[x],{x,2}]+ C2*D[e[x],{x,4}]- C3*D[θ[x],
{x,4}] + C4 D[θ[x],{x,6}];
eq2=-s*a (s^2 β + ϵ1*ϵ2)*e[x] - s*a*θ[x] +
b1*g[x] + (1 +s*a*β)*(w*D[e[x], {x, 2}]+β*D[θ[x], {x, 4}]);
eq3=b3*s^2*e[x]-(b2 + b*s)*g[x]-b3*(s^2*β+ w)*D[e[x], {x, 2}] + D[g[x],
{x, 2}] + b3*β*w*D[e[x], {x, 4}] - b3*β*D[θ[x], {x, 4}] +
b3*β^2*D[θ[x], {x, 6}];
It is suppose to obtain a six order ODE in $θ[x]$ but I could not simplify this system or to solve even with the following DSolve command:
DSolve[eq1==0,eq2==0,eq3==0,{θ[x],e[x],g[x]},{x}]
it gives no response. I tried to use the command Reduce, but Mathematica gives no response too. If there is no any syntax mistakes, would some one suggests what do can I do? Thank you. In this system the only functions are $θ[x]$, $e[x]$ and $g[x]$, and all other characters are non zero constants.
D[θ[x], {x,2}]=A1 θ[x]+A2 e[x]-A3 g[x]; D[e[x], {x,2}]=B1 θ[x]+B2 e[x]-B3 g[x]; D[g[x], {x,2}]=C1 θ[x]+C2 e[x]-C3 G[x]
where A1,...,C3 are constants. it is not slove also with DSolve. $\endgroup$