Originally Posted by

**fifthrapiers** I have to solve the given Dif. EQs with the initial conditions that are given.

But, the hard part is I'm not allowed to use the same method twice. (That is, I can only use separation of variables once, variation of parameters once, etc).

1.) $\displaystyle (1 + t^2)\frac{dy}{dt} = 2ty + 2, y(0) = -2$

2.) $\displaystyle y''' - y'' - 2y' = e^{-t} + 3e^{2t}, y(0) = 1, y'(0) = \frac{-13}{6}, y''(0) = \frac{-5}{3}$

3.) $\displaystyle \frac{dy}{dt} = \frac{t^2}{y + t^3y}, y(0) = -2$

4.) $\displaystyle y'' + 4y' + 4y = t^{-2}e^{-2t}, y(1) = 0, y'(1) = 0$