Originally Posted by

**i_zz_y_ill** The question is find the solution of:

$\displaystyle x^2\frac{dy}{dx}-x\frac{dy}{dx}-8y=1+x$

clearly the coefficients in what i would write down to be the auxilliary equation are not constants. Ive been told by my solution to use y=$\displaystyle x^m$ but i dont see how this gives(in the solutions) $\displaystyle m(m-1)-m-8=x^2-2m-8=(x-4)(x+2)0$

giving m=4 or m=-2. and the corrosponding complementary function. Does anyone have any ideas or could show me how the method actually cancels out the non constant coefficeints? thanks. oh i think you are supposed to use liebnitz?? not sure