[SOLVED] Differential equation

superman69 · #1 $Old$ November 4th, 2009, 07:55 PM

Find the function

that satisfies the differential equation

and the condition

.

So first of all I found integration factor which is

Then I plugged it in for the general solution formula.

which came out to be

y=

∫

6

dt+C

then it came out to be

+C

then I plugged in the values and got C=1 but all the work done wasn't correct

BobP · #2 $Old$ November 5th, 2009, 06:44 AM

When you multiply by the integrating factor, the equation becomes
$e^{-t^{2}}\frac{dy}{dt}-2te^{-t^{2}}y=6t^{2}.$
Integrating, you get
$e^{-t^{2}}y=2t^{3}+C,$ so
$y=e^{t^{2}}(2t^{3}+C),$ etc. .