What is the solution for y^{''}-2y^'+13y=0 ?

The solution for y^{''}-2y^'+13y=0 is y=e^t(c_{1}cos(2sqrt(3)t)+c_{2}sin(2sqrt(3)t))

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y^{''}-2y^'+13y=0

y^{^{''}} - 2 y^{^{'}} + 13 y = 0

y = e^{t} (c_{1} cos (23 t) + c_{2} sin (23 t))

Solution steps

y^{''} (t) - 2 y^{'} (t) + 13 y = 0

Solve linear ODE:

y = e^{t} (c_{1} cos (23 t) + c_{2} sin (23 t))

y = e^{t} (c_{1} cos (23 t) + c_{2} sin (23 t))

y^{^{''}} - 22 y^{^{'}} = 0

y^{^{''}} + 9 y^{^{'}} + 17 y = 0

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

y^{^{''}} + 4 y^{^{'}} + y 5 = 0

y^{^{''}} + 8 y^{^{'}} + 15 y = 0, y (0) = - 2, y^{^{'}} (0) = 16

What is the solution for y^{''}-2y^'+13y=0 ?
The solution for y^{''}-2y^'+13y=0 is y=e^t(c_{1}cos(2sqrt(3)t)+c_{2}sin(2sqrt(3)t))