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
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 $y$.