What is the solution for 15y^{''}+90y^'+135y=0,y(0)=3,y^'(0)=0 ?

The solution for 15y^{''}+90y^'+135y=0,y(0)=3,y^'(0)=0 is y=3e^{-3t}+9te^{-3t}

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15y^{''}+90y^'+135y=0,y(0)=3,y^'(0)=0

15 y^{^{''}} + 90 y^{^{'}} + 135 y = 0, y (0) = 3, y^{^{'}} (0) = 0

y = 3 e^{- 3 t} + 9 t e^{- 3 t}

Solution steps

15 y^{''} (t) + 90 y^{'} (t) + 135 y = 0

Solve linear ODE:

y = 3 e^{- 3 t} + 9 t e^{- 3 t}

y = 3 e^{- 3 t} + 9 t e^{- 3 t}

12 y^{^{''}} + 64 y = 0, y (0) = 4, y^{^{'}} (0) = 7

y^{^{''}} + 8 y^{^{'}} + 25 y = 0, y (0) = 0, y^{^{'}} (0) = 0.9

y^{^{''}} - 8 y^{^{'}} + 25 y = 0, y (0) = e^{4 x} cos (3 x)

81 y^{^{''''}} = 256 y

\frac{d ^{2} y}{d x ^{2}} = 16 y

What is the solution for 15y^{''}+90y^'+135y=0,y(0)=3,y^'(0)=0 ?
The solution for 15y^{''}+90y^'+135y=0,y(0)=3,y^'(0)=0 is y=3e^{-3t}+9te^{-3t}