(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

y'=1+x+y+xy, y(0)=0

2. Relevant equations

[itex]\frac{dy}{dx}[/itex]+P(x)y=Q(x)

[itex]\rho[/itex](x)=e^{[itex]\int(P(x)dx)[/itex]}

3. The attempt at a solution

My main problem is correctly getting it into the form, [itex]\frac{dy}{dx}[/itex]+P(x)y=Q(x). I know what to do from there.

First, I tried y'-(y+xy)=1+x, where P(x)=1+x [itex]\rightarrow[/itex] [itex]\rho[/itex](x)=e^{[itex]\int(1+x)[/itex]}=e^{x+x2/2}.

When i multiply both sides by [itex]\rho[/itex](x), i don't come out with anything that i can easily integrate. Any suggestions would be much appreciated!

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# Homework Help: First-Order Linear Differential Equation

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