Linear equations: dP/dt + 2tP = P + 4t - 2

[mares0909]

I have this problem:

dP/dt + 2tP = P + 4t - 2

So I grouped dP/dt + (2t-1)P = 4t - 2

Then I have that P(x) = 2t-1= S 2t-1 dt = t^2 - t = e^(t^2 - t )

So

Y (e^(t^2 - t )) = S (e^(t^2 - t ))(4t-2) dt

Im stuck here because when I integrate the right hand side I cant integrate the e part of it.

Thank you.

 

[tkhunny]

You are SO CLOSE!!!!

Try \(\displaystyle u = t^{2} - t\)

You may wish to note that \(\displaystyle 4t - 2 = 2(2t-1)\).