Identify the types of differential equation, such as linear/nonlinear, homogeneous/nonhomogeneous.

solve the initial value problem

determine the interval of existence, if you can find an explicit solution

1. y' + 2ty = 4t, y(0) = -4

2. y' + 2y = e^-t + t + 1, y(-1) = e

3. dy/dt + 1/t*y = ty^2

4. y' = -y + ty^-2, y(0) = 2

5. t^2y' + sec y = 0, y(-1) = 0

6. (2y - sin y)y' + t = sint, y(0) = 0