What is the solution for y^{''}+3y^'+12y=0 ?

The solution for y^{''}+3y^'+12y=0 is y=e^{-(3t)/2}(c_{1}cos((sqrt(39)t)/2)+c_{2}sin((sqrt(39)t)/2))

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y^{''}+3y^'+12y=0

y^{^{''}} + 3 y^{^{'}} + 12 y = 0

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{39 t}{2}) + c_{2} sin (\frac{39 t}{2}))

Solution steps

y^{''} (t) + 3 y^{'} (t) + 12 y = 0

Solve linear ODE:

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{39 t}{2}) + c_{2} sin (\frac{39 t}{2}))

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{39 t}{2}) + c_{2} sin (\frac{39 t}{2}))

What is the solution for y^{''}+3y^'+12y=0 ?
The solution for y^{''}+3y^'+12y=0 is y=e^{-(3t)/2}(c_{1}cos((sqrt(39)t)/2)+c_{2}sin((sqrt(39)t)/2))