Solve the following problems. Identify the type of differential equation, show your work and provide all explanations. 1. x2y + 2xy = y/2. 2. y' + 4y' - 5y = 2e*. Use the method of undetermined coefficients. 3. y" + y' + 3y = 1 - 5cosx 4. Find the form of power series solutions near x = 0. Provide complete analysis. Do not evaluate the coefficients of the series or look for recurrence relations. 2xy" + (x + 5)y' - y = 0. 5. Use Laplace transform to solve the following equation: tx" + (2t - 1)x' + 2x = 0, x= x(t), x(0) = 0. 379 1 C