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## Homework Statement

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

## Homework Equations

[tex]yT =\int{QT}dx + C[/tex]

where T is the intergrating factor

T = [tex]e^{\int{P}dx[/tex]

and P is the co-efficient of y from the differential equations

## The Attempt at a Solution

well to find T we need to do:

[tex]e^{\int{\frac{1}{2x}}}dx[/tex]

[tex]e^{\frac{1}{2}\int{\frac{1}{x}}}dx[/tex]

[tex]e^{\frac{1}{2}ln|x|}[/tex]

[tex] = x^{\frac{1}{2}}[/tex]

so using [tex]yT =\int{QT}dx + C[/tex]

you get

[tex] yx^{\frac{1}{2}}= \int{x^{\frac{1}{2}x^-{\frac{1}{2}}}dx[/tex]

[tex] yx^{\frac{1}{2}}= \int{1}dx[/tex]

[tex] yx^{\frac{1}{2}}= x + c[/tex]

the answer in the back of the book says [tex]yx^{\frac{1}{2}} = \frac{1}{2}x^{2}[/tex]

Where have I gone wrong?

Thanks :)