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

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

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(d^2-d)y=e^xcos(x)

(d^{2} - d) y = e^{x} cos (x)

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

Solution steps

(d^{2} - d) y = e^{x} cos (x)

Solve linear ODE:

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

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

y^{^{''}} + 17 y^{^{'}} + 30 y = cos (2 t)

e^{x} y^{^{''}} + 2 e^{x} y^{^{'}} + 5 e^{x} y = sin (2 x)

y^{^{'''}} - 13 y^{^{''}} + 36 y^{^{'}} = 72 e^{x}

y^{^{''}} + 5 y^{^{'}} = x + 2

y^{^{'''}} = 3 y^{^{''}} + 9 \cdot e^{x} + 0 \cdot cos (x)

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