- #1

DryRun

Gold Member

- 838

- 4

**Homework Statement**

dy/dx + y/x = e^(x^2)

Express y in terms of x and arbitrary constant.

**The attempt at a solution**

It is in the standard 1st order linear ODE form.

P(x) = 1/x

Q(x) = e^(x^2)

u(x) = x (after calculation)

So, d(uy)/dx = uQ

d(uy)/dx = x.e^(x^2)

I have to integrate both sides w.r.t.x

Finding the R.H.S is problematic though. As it seems infinite, from what i've understood from my calculations.

Integral of x.e^(x^2) (done by partial integration)

Let U = x, so dU/dx = 1

Let dV = e^(x^2), so V = [e^(x^2)]/2x (is this correct?)

xy = x.[e^(x^2)]/2x - integral of [e^(x^2)]/2x.(1).dx

Then i have to integrate the R.H.S again and again and again, as i can't get rid of e^(x^2) with a multiple of x always in the denominator.

Any advice?