Using an integrating factor properly

[cameuth]

alright guys, I've been trying to tackle this for a couple of hours now.

dy/dt-2y=4-t
my integrating factor is e^(-2t) of course.

dy(e^(-2t))/dt-2ye^(-2t)=4e^(-2t)-te^(-2t)

then I get completely lost. how do I integrate when it's like this? My book simplifies the above equation into

d(e^(-2y))/dt=4e^(-2t)-te^(-2t)

can anyone explain how that simplification occurs??

 

[tiny-tim]

hi cameuth!

(try using the X² button just above the Reply box )

d(e^(-2y))/dt=4e^(-2t)-te^(-2t)

can anyone explain how that simplification occurs??

(you mean d(ye^-2t)/dt )

use the product rule on ye^-2t ​