What is the solution for (D^2-2D+5)^2y=0 ?

The solution for (D^2-2D+5)^2y=0 is y=e^x(c_{1}cos(2x)+c_{2}sin(2x))+xe^x(c_{3}cos(2x)+c_{4}sin(2x))

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(D^2-2D+5)^2y=0

(D^{2} - 2 D + 5)^{2} y = 0

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + x e^{x} (c_{3} cos (2 x) + c_{4} sin (2 x))

Solution steps

(D^{2} - 2 D + 5)^{2} y = 0

Solve linear ODE:

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + x e^{x} (c_{3} cos (2 x) + c_{4} sin (2 x))

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + x e^{x} (c_{3} cos (2 x) + c_{4} sin (2 x))

What is the solution for (D^2-2D+5)^2y=0 ?
The solution for (D^2-2D+5)^2y=0 is y=e^x(c_{1}cos(2x)+c_{2}sin(2x))+xe^x(c_{3}cos(2x)+c_{4}sin(2x))