What is the solution for (D^2-6D+25)y=0 ?

The solution for (D^2-6D+25)y=0 is y=e^{3x}(c_{1}cos(4x)+c_{2}sin(4x))

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(D^2-6D+25)y=0

(D^{2} - 6 D + 25) y = 0

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

Solution steps

(D^{2} - 6 D + 25) y = 0

Solve linear ODE:

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

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

4 y^{^{''}} + 4 y^{^{'}} + y = 0, y (0) = - 1, y^{^{'}} (0) = 2

\frac{d ^{2} y}{d x ^{2}} + 36 y = 0

x^{^{''}} - 2 x^{^{'}} + 5 x = 0

y^{^{''}} + 49 y = 0, y (0) = 5, y^{^{'}} (0) = - 7

y^{^{''}} + y = 0, y (π) = 0, y (0) = 0

What is the solution for (D^2-6D+25)y=0 ?
The solution for (D^2-6D+25)y=0 is y=e^{3x}(c_{1}cos(4x)+c_{2}sin(4x))