What is the solution for (d^2-2d+2)y=3e^xsin(x) ?

The solution for (d^2-2d+2)y=3e^xsin(x) is y=e^x(c_{1}cos(x)+c_{2}sin(x))-(3e^xxcos(x))/2

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(d^2-2d+2)y=3e^xsin(x)

(d^{2} - 2 d + 2) y = 3 e^{x} sin (x)

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) - \frac{3 e ^{x} x cos ( x )}{2}

Solution steps

(d^{2} - 2 d + 2) y = 3 e^{x} sin (x)

Solve linear ODE:

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) - \frac{3 e ^{x} x cos ( x )}{2}

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) - \frac{3 e ^{x} x cos ( x )}{2}

y^{^{''}} + 5 y^{^{'}} + 6 y = 5 e^{3 t}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 e^{2 x}

y^{^{''}} + y^{^{'}} = cos (x)

y^{^{''}} + 4 y = 2

y^{^{''}} + 36 y = 24 sin (6 t)

What is the solution for (d^2-2d+2)y=3e^xsin(x) ?
The solution for (d^2-2d+2)y=3e^xsin(x) is y=e^x(c_{1}cos(x)+c_{2}sin(x))-(3e^xxcos(x))/2