What is the solution for y^{''}-6y^'+15y=0 ?

The solution for y^{''}-6y^'+15y=0 is y=e^{3t}(c_{1}cos(sqrt(6)t)+c_{2}sin(sqrt(6)t))

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y^{''}-6y^'+15y=0

y^{^{''}} - 6 y^{^{'}} + 15 y = 0

y = e^{3 t} (c_{1} cos (6 t) + c_{2} sin (6 t))

Solution steps

y^{''} (t) - 6 y^{'} (t) + 15 y = 0

Solve linear ODE:

y = e^{3 t} (c_{1} cos (6 t) + c_{2} sin (6 t))

y = e^{3 t} (c_{1} cos (6 t) + c_{2} sin (6 t))

55 y^{^{''''}} + 136 y^{^{''}} + 25 y = 0

16 y^{^{''''}} = 81 y

f^{^{''}} (x) + f (x) = 0

x^{^{''}} + 14 x^{^{'}} + 49 x = 0

y^{^{''}} + 4 y = 0, y^{^{'}} (π) = 0, y (0) = 0

What is the solution for y^{''}-6y^'+15y=0 ?
The solution for y^{''}-6y^'+15y=0 is y=e^{3t}(c_{1}cos(sqrt(6)t)+c_{2}sin(sqrt(6)t))