Each differential equation has a particular solution that doesn't have a easy guess.
Find a particular solution for each equation using variation of parameters.
No initial conditions are given because you are only asked to find one solution.
There is only one question because there have been parsing errors with the solutions and many of the variation of parameters problems are complicated to parse.
Please enter any multiplication explicitly with * symbols so the parcer can understand your answer, like this:
Use variation of parameters to find a particular solution for the DE below. e^t and (t+1) are homogeneous solutions.