What is the solution for 5y^{''}+30y^'+45y=0,y(0)=-8,y^'(0)=0 ?

The solution for 5y^{''}+30y^'+45y=0,y(0)=-8,y^'(0)=0 is y=-8e^{-3t}-24e^{-3t}t

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5y^{''}+30y^'+45y=0,y(0)=-8,y^'(0)=0

5 y^{^{''}} + 30 y^{^{'}} + 45 y = 0, y (0) = - 8, y^{^{'}} (0) = 0

y = - 8 e^{- 3 t} - 24 e^{- 3 t} t

Solution steps

5 y^{''} (t) + 30 y^{'} (t) + 45 y = 0

Solve linear ODE:

y = - 8 e^{- 3 t} - 24 e^{- 3 t} t

y = - 8 e^{- 3 t} - 24 e^{- 3 t} t

y^{^{''}} + 5 y^{^{'}} + 3 y = 0, y (0) = 5, y^{^{'}} (0) = 7

9 \frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} = 0

y^{^{''}} = 5 y^{^{'}} - 6 y

y^{^{''}} - c^{2} y = 0

2 y^{^{''}} - 2 y^{^{'}} - 2 y = 0

What is the solution for 5y^{''}+30y^'+45y=0,y(0)=-8,y^'(0)=0 ?
The solution for 5y^{''}+30y^'+45y=0,y(0)=-8,y^'(0)=0 is y=-8e^{-3t}-24e^{-3t}t