Linear DE

1. Jan 30, 2007

nateshoe

1. The problem statement, all variables and given/known data[/b]
y'=4x–y+4; y(0)=8

2. The attempt at a solution[/b]
This is simply a first-order DE
So:

y'+y=4x+4
P(x)=1
Q(x)=4x+4
p(x)=e^x
So that ends up being:

ye^x=(4xe^x+4e^x)dx

Integration:
ye^x=4xe^x-4e^x+4e^x

ye^x=4xe^x
divide by e^x
y=4x+C
y=4x+8

However it tells me I'm wrong. either I'm very stupid or I'm going about this completely wrong.

Thanks,
Nate

2. Jan 30, 2007

mjsd

note after the integration, you pick up a constant
$$y e^x = 4 x e^x + C$$

3. Jan 30, 2007

nateshoe

Appreciate it!