What is the solution for (d^2-2d+2)y=4x-2+2e^xsin(x) ?

The solution for (d^2-2d+2)y=4x-2+2e^xsin(x) is y=e^x(c_{1}cos(x)+c_{2}sin(x))+2x+1-e^xxcos(x)

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(d^2-2d+2)y=4x-2+2e^xsin(x)

(d^{2} - 2 d + 2) y = 4 x - 2 + 2 e^{x} sin (x)

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + 2 x + 1 - e^{x} x cos (x)

Solution steps

(d^{2} - 2 d + 2) y = 4 x - 2 + 2 e^{x} sin (x)

Solve linear ODE:

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + 2 x + 1 - e^{x} x cos (x)

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + 2 x + 1 - e^{x} x cos (x)

y^{^{''}} - 12 y^{^{'}} + 36 y = 36 x + 4

y^{^{''}} - 2 y^{^{'}} = 30 e^{- 3 t}, y (0) = 1, y^{^{'}} (0) = 0

2 y^{^{''}} + a y^{^{'}} + a y = e^{- 2 x} + x

y^{^{''}} + 2 y^{^{'}} + 2 y = 4 e^{- x} sec^{3} (x)

y^{^{''}} + 36 y = 36 sec^{2} (6 t)

What is the solution for (d^2-2d+2)y=4x-2+2e^xsin(x) ?
The solution for (d^2-2d+2)y=4x-2+2e^xsin(x) is y=e^x(c_{1}cos(x)+c_{2}sin(x))+2x+1-e^xxcos(x)