As you said, The integrating factor is
Multiply through:
Integrating 'negates' the derivative on the left:
Divide by and remember the log laws:
the problem goes..
The integrating factor for the ODE dxdt - 2xt = t is the integrating factor e*(-2integral(tdt)) = e^-t^2
multiplying the ODE by the integrating factor:
ddt((e^-t^2)*x) = t(e^-t^2)
integrate : e^-t^2 = -0.5(e^-t^2) + c
how does one get the integation bit?? i cant understand it at all =( .. especially the -0.5 ( .... ) +c bit
i tried by parts..but =S.. i end up integrating again and again....and again =| wow
what do you mean by 'negates'? [sorry if its a stupid simple question!]
i can see how if i differentiate..i get the original equation.. but i cannt see how to integrate it yet! =(
if i do it by parts... i have to keep integrating forever...
do you just see the answer clearly by looking?