What is the solution for y^{''}+12y^'+45y=0 ?

The solution for y^{''}+12y^'+45y=0 is y=e^{-6t}(c_{1}cos(3t)+c_{2}sin(3t))

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y^{''}+12y^'+45y=0

y^{^{''}} + 12 y^{^{'}} + 45 y = 0

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

Solution steps

y^{''} (t) + 12 y^{'} (t) + 45 y = 0

Solve linear ODE:

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

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

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What is the solution for y^{''}+12y^'+45y=0 ?
The solution for y^{''}+12y^'+45y=0 is y=e^{-6t}(c_{1}cos(3t)+c_{2}sin(3t))