How do you solve the differential equation dy/dx = xe^-x?

[n.a.s.h]

Homework Statement

solve the diferential equation: dy/dx = xe^-x

Homework Equations

The Attempt at a Solution

dy/dx = xe^-x

dy = xe^-x dx
∫dy = ∫(xe^-x) dx

u = x and v ' = e^-x


That is all i really know to do I'm really confused and any help is appreciated.

 

[Ted123]

Homework Statement

solve the diferential equation: dy/dx = xe^-x

Homework Equations

The Attempt at a Solution

dy/dx = xe^-x

dy = xe^-x dx
∫dy = ∫(xe^-x) dx

u = x and v ' = e^-x


That is all i really know to do I'm really confused and any help is appreciated.

$\frac{dy}{dx} = xe^{-x}$

$\int dy = \int xe^{-x}\;dx$ (*)

$y= \cdots$

the RHS of line (*) can be integrated by parts.

With $u=x,\;u'=1,\;v'=e^{-x},\; v=-e^{-x}$

Then $\int v'u\;dx = uv - \int u'v\;dx$

Once you've done that you've got your general solution (y=...) and don't forget the all important constant of integration.