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

The solution for (d^2-2d+4)y=e^xcos(x) is y=e^x(c_{1}cos(sqrt(3)x)+c_{2}sin(sqrt(3)x))+1/2 e^xcos(x)

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + (\frac{3}{4}) y = 3 e^{x} + (\frac{9}{2}) x

y^{^{''}} + 4 y = cos (x)

(d^{4} + d^{3} + d^{2}) y = 5 x^{2} + cos (x)

(d^{4} + d^{3} + d^{2}) y = 5 x^{2}

(d^{3} - 3 d^{2} + 3 d - 1) y = sin (x) + x^{3}

What is the solution for (d^2-2d+4)y=e^xcos(x) ?
The solution for (d^2-2d+4)y=e^xcos(x) is y=e^x(c_{1}cos(sqrt(3)x)+c_{2}sin(sqrt(3)x))+1/2 e^xcos(x)