Question

we are to find the power series solution for y'=xy.

I have calculated to the point that I believe the answer is c_0/2^n*n! First of all is this correct and secondly, how do I write the solution in terms of c_0 * summation of something in terms of x^n?

Answer 1

dy/y = x dx
ln y = x^2/2 + c
y = C e^(.5 x^2)
so what is e^(.5 x^2)
well e^z = 1 + z + z^2/2! + z^3/3! +......
so
C [ 1 + .5x^2 + .25x^4/2! .....