# First-order Taylor series expansion

I have a first-order equation that is supposed to be solved using the Frobenius method. I am having some difficulty since the equation is not equal to zero. I would appreciate any help.

y' + (1 - x^2)y = x

• I don't know the solution, but I think you can use the euler's method? hopefully you are given the initial condition and use step sizes to determine how accurate. – johnson Nov 2 '16 at 12:04

If you are looking for a Taylor series solution, then you can simply differentiate the equation and plug in your initial $x_0$ and solve for the values of the derivatives of $y$. You can do this for as many derivatives as you need to construct the Taylor series for $y$.