Solving First Order ODE with Integrating Factor

[bobred]

Homework Statement

Solve first order ODE

Homework Equations

\frac{dy}{dx}=x^2+1+\frac{2}{x}y
Rearranged
\frac{dy}{dx}-\frac{2}{x}y=x^2+1

The Attempt at a Solution

Integrating factor
p=\exp(-\int \frac{2}{x})=\exp(-2\ln x)=x^{-2}

Multiplying through by the integrating factor
\frac{d}{dy}(x^{-2}y)=x^{-2}

Integrating both sides
x^{-2}y=-x^{-1}+C

Dividing through by x^{-2}
y=Cx^2-x

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

y=x^3+Cx^2-x

Any ideas? Thanks

 

[HallsofIvy]

Homework Statement

Solve first order ODE

Homework Equations

\frac{dy}{dx}=x^2+1+\frac{2}{x}y
Rearranged
\frac{dy}{dx}-\frac{2}{x}y=x^2+1

The Attempt at a Solution

Integrating factor
p=\exp(-\int \frac{2}{x})=\exp(-2\ln x)=x^{-2}

Multiplying through by the integrating factor
\frac{d}{dy}(x^{-2}y)=x^{-2}

No, the right hand side of your original equation was x^2+ 1. Multiplying that by x^{-2} gives 1+ x^{-2}. You've dropped the "1".

Integrating both sides
x^{-2}y=-x^{-1}+C

Dividing through by x^{-2}
y=Cx^2-x

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

y=x^3+Cx^2-x

Any ideas? Thanks

 

[bobred]

Thanks