- #1
bobred
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Homework Statement
Solve first order ODE
Homework 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]
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