Please answer the following questions:-
For each of the following, solve the initial value problem using the method of Laplace transforms. y"-3y'+2y = cos t y(0) = 0 y'(0) = -l y"'+4y"+y'-6y = -12 y(0) = 1 y'(0) = 4 y"(0) = -2 Use the convolution theorem to find the inverse Laplace transform of the following function. F(s) = 11s/(s2 +121)2 Solve the following equation. (y - x)dx + (x + y)dy = 0 Find the general solution to the following differential equation. d2y/dx2 + 4dy/dx + 5y = e-x -sin2x Obtain the general solution to the following differential equation dy/dx - y/x = xex
Show transcribed image text For each of the following, solve the initial value problem using the method of Laplace transforms. y"-3y'+2y = cos t y(0) = 0 y'(0) = -l y"'+4y"+y'-6y = -12 y(0) = 1 y'(0) = 4 y"(0) = -2 Use the convolution theorem to find the inverse Laplace transform of the following function. F(s) = 11s/(s2 +121)2 Solve the following equation. (y - x)dx + (x + y)dy = 0 Find the general solution to the following differential equation. d2y/dx2 + 4dy/dx + 5y = e-x -sin2x Obtain the general solution to the following differential equation dy/dx - y/x = xex