# Question:How expand in perturbation series in maple?

## Question:How expand in perturbation series in maple?

Maple 2018

I have the following ODE perturbation problem which I want maple to solve for me:

q'(\tau)=f(p(eps*\tau)+eps*q(\tau),r(eps*\tau)+s(\tau))-f(p(eps*\tau,r(eps*\tau)+s(\tau))-f(p(eps*\tau),r(eps*\tau))

where q(\tau)=q_0(\tau)+eps*q_1(\tau)

p(eps*\tau)=p_0(eps*\tau)+eps*p_1(eps*\tau)

s(\tau)=s_0(\tau)+eps*s_1(\tau)

r(eps*\tau)=r_0(eps*\tau)+eps*r_1(eps*\tau)

I want maple to expand every function that depends on eps in its arguments by a Taylor series around eps=0, i.e h(eps)=h(0)+eps*h'(0)

and also expand the difference above the fs with an eps-expansion around eps=0.

I did all this manually now I want to check if my calculations are correct, eventaully I want to equate same powers of eps of the RHS and LHS of the first ODE I wrote above.

Then how to use maple for this?

Thnaks.

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