What is the solution for 3/2 y^{''}+3y^'+15y=0 ?

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

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3/2 y^{''}+3y^'+15y=0

\frac{3}{2} y^{^{''}} + 3 y^{^{'}} + 15 y = 0

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

Solution steps

\frac{3}{2} y^{''} (t) + 3 y^{'} (t) + 15 y = 0

Solve linear ODE:

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

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

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