Solve the following questions. Solve the differential equation by variation of p

Question

Solve the following questions.

Solve the differential equation by variation of parameters. 2y"+ y'-y=x+1 Consider the differential equation ay" + by' + cy = g(x), where a, b, and are constants. Choose the input functions g(x) for which the method of undetermined coefficients is applicable and input functions for which the method of variation of parameters is applicable. Explain the reason for each choice. g(x) = exlnx g(x) = x3 cosx g(x) = sinx/ex g(x) = 2x-2ex g(x) = sin2x g(x) = ex/sinx Solve the initial-value problem d2y/dx2 + 4dy/dx + 5y = 0, with y(0) = 0, y'(0) = 3.

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