What is the solution for (d^2-2d+5)y=e^x ?

The solution for (d^2-2d+5)y=e^x is y=e^x(c_{1}cos(2x)+c_{2}sin(2x))+1/4 e^x

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(d^2-2d+5)y=e^x

(d^{2} - 2 d + 5) y = e^{x}

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{1}{4} e^{x}

Solution steps

(d^{2} - 2 d + 5) y = e^{x}

Solve linear ODE:

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{1}{4} e^{x}

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{1}{4} e^{x}

What is the solution for (d^2-2d+5)y=e^x ?
The solution for (d^2-2d+5)y=e^x is y=e^x(c_{1}cos(2x)+c_{2}sin(2x))+1/4 e^x