(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# First Order ODE

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