- #1

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I have the first order differential equation [tex]y+y' = x[/tex]

y(0) = 0

First i tried to assume a solution of the form Ax+b, that didn't quite work.

Then i tried to use the Integrating factor technique, work follows

[tex]e^{\int1} = e^x[/tex]

[tex]\int e^x(y+y') = \int{xe^x}[/tex]

[tex] ye^x = \int xe^x[/tex]

let u = x, du=1

v = e^x dv=e^x

So i end up with:

[tex] ye^x = xe^x -e^x[/tex]

which is wrong...

Any ideas?