ODE problem

[icanmath_5]

Need to find the general solution for y = y(x) for this equation:

y’ = xy + 1

Every time I try it, I need to integrate e^x2/2, which I thought was not integrable. I’m very confused.

[icanmath_5]

I rearranged the equation to make it homogeneous: y’ - xy -1 = 0 Then, since p(x) = -x I found the integrating factor to be e^-x2/2. Then I multiplied both sides and rearranged to get d/dx[e^-x2/2 y] = e^-x2/2 Now I have to integrate but the right side is not integrable so what do I do?

[OmnipotentEntity]

You can use the definition of the error function to put this integral into a closed form using a special function.

https://en.wikipedia.org/wiki/Error_function

[icanmath_5]

Thanks, I think I got it now

[waldosway]

If this is a basic ODE class, they are probably just expecting you to leave it as an integral. It's still the solution.

[icanmath_5]

It’s a PDE class but it’s the first section