- #1
DryRun
Gold Member
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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?
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?