Question

Just curious about this one: how would I solve \(xy'+y\ln(x) = x\ln(y)\)?

Answer 1

@Kainui

Answer 2

@Kainui :)

Answer 3

By simplify do you mean solve the differential equation?

Answer 4

Yeah

Answer 5

Ok what have you tried, substitution, separation, etc?

Answer 6

separation wouldnt work very nicely... I dont think considering the natural log functions

Answer 7

substitution?

Answer 8

can't use integrating factor that's for sure.

Answer 9

first order ode has 5 techniques doesn't it?
separation of variables
integrating factor
substitution
homogeneous
exact

Answer 10

I can't even use integrating factor due to the ln y
I need the equation in the form of
dy/dx = p(x)y=q(x) so that's out

Answer 11

separation of variables needs to be in the form of h(y) dy = f(x) dx meaning I need all of my x terms on the right and all the y terms on the left

Answer 12

Hmm..that could possibly work, right?