@Carl Love Thank you.But on my computer it took about 30 minutes.Why?

@Carl Love Thank you for reminding

@Markiyan Hirnyk My difficulty is that integration spend time too long , not series expansion.Thank you!

@Preben Alsholm Yes,you right.Howvere,how to solve the error? or solving the equation ode with other numerical algorithms in maple?Thank you.

Thank you for your help.But I have another question.How to invlaplace the following expression？
>res:=1/(s^2)*(exp((1/2)*C3+(1/2)*sqrt(C3^2+4*C1*s)+eta*sqrt(C3^2+4*C1*s))-exp((1/2)*C3+(1/2)*sqrt(C3^2+4*C1*s))+exp(sqrt(C3^2+4*C1*s))-exp(eta*sqrt(C3^2+4*C1*s)))*(-s+exp(C4))*(Sum(-e^(sqrt(C3^2+4*C1*s)*k), k = 0 .. infinity))*exp(-(1/2*(C3+sqrt(C3^2+4*C1*s)))*eta)

Thank you for your help.But I have another question.How to invlaplace the following expression？
>res:=1/(s^2)*(exp((1/2)*C3+(1/2)*sqrt(C3^2+4*C1*s)+eta*sqrt(C3^2+4*C1*s))-exp((1/2)*C3+(1/2)*sqrt(C3^2+4*C1*s))+exp(sqrt(C3^2+4*C1*s))-exp(eta*sqrt(C3^2+4*C1*s)))*(-s+exp(C4))*(Sum(-e^(sqrt(C3^2+4*C1*s)*k), k = 0 .. infinity))*exp(-(1/2*(C3+sqrt(C3^2+4*C1*s)))*eta)

Thank you very much!It is very helpfull.

Thank you very much!It is very helpfull.

Thank you very

Thank you very

Thank you for your well replay

Thank you for your well replay

@Markiyan Hirnyk Yes，you are right.Moreover,now if I only want to konw all the residue of res,how to do this?

@Markiyan Hirnyk Yes，you are right.Moreover,now if I only want to konw all the residue of res,how to do this?

Yes,, the integral of res over the reals diverges.But if on complex?