What is the solution for y^{''}-12y^'+54y=0 ?

The solution for y^{''}-12y^'+54y=0 is y=e^{6t}(c_{1}cos(3sqrt(2)t)+c_{2}sin(3sqrt(2)t))

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y^{''}-12y^'+54y=0

y^{^{''}} - 12 y^{^{'}} + 54 y = 0

y = e^{6 t} (c_{1} cos (32 t) + c_{2} sin (32 t))

Solution steps

y^{''} (t) - 12 y^{'} (t) + 54 y = 0

Solve linear ODE:

y = e^{6 t} (c_{1} cos (32 t) + c_{2} sin (32 t))

y = e^{6 t} (c_{1} cos (32 t) + c_{2} sin (32 t))

What is the solution for y^{''}-12y^'+54y=0 ?
The solution for y^{''}-12y^'+54y=0 is y=e^{6t}(c_{1}cos(3sqrt(2)t)+c_{2}sin(3sqrt(2)t))