# First Order ODE

1. Sep 11, 2011

### swtjuice

1. The problem statement, all variables and given/known data

Find the following IVP Diff.Eq.
xyy'=x^2+3y^2
y(1)=2
2. Relevant equations

3. The attempt at a solution
I've been struggling with this problem for a while now. I believe I have figured out it is homogenous, thus y=ux substitution applies.
Through some work I have arrived at the answer of
ln x +C=ln(2u^2+1)/4, re-substituting u=y/x I get the answer of
y^2= C*x^3-x^2/2 where C=4.5 based on the IVP.
When I plot this against the ODE solution in MATLAB, the answers do not agree.
Am I wrong that this diff. eqn is homogenous, I believe I have checked my algebra several times. Any help or tips would be great.

2. Sep 11, 2011

### LCKurtz

You are correct that the equation is homogeneous and that substitution should work. One thing you can try is substitute your solution back into the equation and boundary conditions. If it checks you are home free and if it doesn't, time to check for errors :grumpy:

3. Sep 11, 2011

### swtjuice

Great, Hopefully my matlab code is the problem. I've been trying to find errors in this problem for a while now. Thanks again

4. Sep 12, 2011

### ehild

the blue is correct, but the red is wrong. You made a mistake when removing the logarithm or substituting u=y/x back. Show work in detail.

ehild

5. Sep 12, 2011

### Ray Vickson

What is the DE for z = y^2?

RGV