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