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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + y - 2 e^{- t} - 1 = 0

\frac{d ^{2}}{d x ^{2}} (θ (x)) + 4 θ (x) = csc^{2} (2 x)

(D^{4} + D^{2}) y = 3 x^{2} + 4 sin (x) - 2 cos (x)

y^{^{''}} + 2 y = - 18 x e^{2 x}

y^{^{''}} - y^{^{'}} - 6 y = 2 cos (x) - 2 e^{3 x} + 10

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