(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve first order ODE

2. Relevant equations

[tex]\frac{dy}{dx}=x^2+1+\frac{2}{x}y[/tex]

Rearranged

[tex]\frac{dy}{dx}-\frac{2}{x}y=x^2+1[/tex]

3. The attempt at a solution

Integrating factor

[tex]p=\exp(-\int \frac{2}{x})=\exp(-2\ln x)=x^{-2}[/tex]

Multiplying through by the integrating factor

[tex]\frac{d}{dy}(x^{-2}y)=x^{-2}[/tex]

Integrating both sides

[tex]x^{-2}y=-x^{-1}+C[/tex]

Dividing through by [tex]x^{-2}[/tex]

[tex]y=Cx^2-x[/tex]

The problem comes when I use say, Maple to check the answer, it gives

[tex]y=x^3+Cx^2-x[/tex]

Any ideas? Thanks

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# Homework Help: First order ODE solution

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