I have this problem:
(x'+x''+epsilon/x)(x'-(x')^3/3!)(x''-(x'')^3/3!)(epsilon/x -(epsilon/x)^3/3!)=1
x(0)=epsilon , x'(epsilon)=epsilon+epsilon^{-1}
0<epsilon<<1
Now I want to try the ansatz: x(epsilon,t)=x_{-1}(t)/epsilon+x_0(t)+x_1(t)epsilon.
Can you suggest me a way to implement this ansatz (i.e finding x_{-1}(t),x_0(t),x_1(t)).
Appreciate your time!