1. Solve the following initial value problem for the function y(x). 2. Find a general solution y(x) to the differential equation y2x2 3. Given the function y(x)Ce C2e cosx a) Prove that it is a solution to the equation y"- 3y" + 4y'-2y 0 b) Show that the initial value problem y(0)-1; y (0)0;y0)0 has no solution. 4. Find a general solution y(x) to the equation y"- 2y ye 5. Find a general solution y(x) to the equation y" -2y 2y e* 6. Find the solution y(t) to the following initial value problem using the Laplace transform method: y" - y-6y 0 7. Solve the initial value problem (6) using another method.