So, I am taking DE again, well just retaking the exam (medical reasons!) so I am trying to follow along with the current course while I am away from school. But... I'm stuck already! I think I'm just stuck on the algebra... but maybe someone can point out what I'm doing wrong:
dy/dx = y/x + (x^2)*e^(y/x)
We are asked to show that this tranforms into dv/dx = x * e^v via the substitution v=y/x. Okay... sounds easy!
dy/dx = v + x^2 * e^v
I need to get rid of the dy somehow... and from v=y/x -> dy/dx = v
So now, v = v + x^2 * e^v
x^2 * e^v = 0 ?!
dy/dx = y/x + (x^2)*e^(y/x)
We are asked to show that this tranforms into dv/dx = x * e^v via the substitution v=y/x. Okay... sounds easy!
dy/dx = v + x^2 * e^v
I need to get rid of the dy somehow... and from v=y/x -> dy/dx = v
So now, v = v + x^2 * e^v
x^2 * e^v = 0 ?!
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