Question

Solve the initial value problem
12(t+1)(dy/dt)−8y=32t,

for t>−1 with y(0)=3.

Answer 1

is this a separable equation?

Answer 2

ODE?

Answer 3

yes its a differentia eq

Answer 4

i have an integrating factor of (t+1)^(-2/3) is that correct

Answer 5

integrating factor

Answer 6

i think there is a simpler way but im not sure

Answer 7

integrating factor is \[\huge e^{\int -\frac{2}{3(t+1)}}\] not just integrand

Answer 8

that simplifies to (t+1)^(-2/3) though correct?

Answer 9

oh yea, you are right, hehehe. I am sorry.

Answer 10

okay, so im at a part where i have to integrate \[\frac{ t }{ (t+1)^{5/3} }\]

Answer 11

how would i do this