how to solve this:
An approximate solution of the problem $y^"-y^{'}+4x\epsilon^x =0$, $y^{'}(0)-y(0)=1$,$y^{'}(1)+y(1)=-\epsilon$ is: here we have to calculate the value of y(x)?
what i did is: for this we use rayleigh-Ritz method, and i got the function $f(x,y,y^{'},y^{"})=y^{'2}+y^2-8x\epsilon ^x y^{"}$
i assumed the function y(x)=$c_1+c_2x$
how to proceed further and the answer and am not able to get the correct value of the constants?