# Homework Help: A hard differential equation - where is the error in my logic?

1. Jun 1, 2012

### Nikitin

[SOLVED] A hard differential equation - where is the error in my logic?

1. The problem statement, all variables and given/known data
2xyy' + y2, where y is a function of x

3. The attempt at a solution

2xyy' + y2 = 12x2 |*(1/x)
=> (y2)' + y2/x =12x |*ln(x), 2yy' = (y2)'
=> (y2ln(x))' = 12x*ln(x)
=> y2ln(x) = ∫12x*ln(x)
=> y2ln(x) = 6x2ln(x) -3x2 + C
=> y = ±sqrt[3x2(2-1/ln(x)) + c/ln(x)]

Well, my result is wrong. Can somebody tell me the error in my logic? HELP, my math exam is on the 4th of June...

Last edited: Jun 1, 2012
2. Jun 1, 2012

### sharks

What is that on the R.H.S. with the vertical bar, etc? Your problem isn't clear.

Assuming that your original ODE is: $2xyy'+y^2=12x^2$
Re-arranging gives: $y'+\frac{1}{2x}y=6xy^{-1}$. You get a Bernoulli equation.

Last edited: Jun 1, 2012
3. Jun 1, 2012

### tt2348

=> (y2)' + y2/x =12x |*ln(x), 2yy' = (y2)'

=> (y2ln(x))' = 12x*ln(x)
(y^2)'*ln(X)+(y^2/x)*ln(x)=/=(y^2*ln(x))'
I believe

4. Jun 1, 2012

### Nikitin

Oh crap, I'm such an idiot! thanks, TT. In addition, I found out how to solve this, so forget about this thread guys!

sharks: I have no idea what a bernoulli equation is, sorry. I haven't even started uni yet.

5. Jun 1, 2012

### Ray Vickson

Re: [SOLVED] A hard differential equation - where is the error in my logic?

$$\frac{d}{dx}(x y^2) = 2 x y y' + y^2.$$

RGV

6. Jun 2, 2012

### dimension10

Then just find out!