What is the solution for y^{''}+10y^'+25y=0,y(0)=0,y^'(0)=-8 ?

The solution for y^{''}+10y^'+25y=0,y(0)=0,y^'(0)=-8 is y=-8e^{-5t}t

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y^{''}+10y^'+25y=0,y(0)=0,y^'(0)=-8

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 0, y^{^{'}} (0) = - 8

y = - 8 e^{- 5 t} t

Solution steps

y^{''} (t) + 10 y^{'} (t) + 25 y = 0

Solve linear ODE:

y = - 8 e^{- 5 t} t

y = - 8 e^{- 5 t} t

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = 10, y^{^{'}} (0) = 27

y^{^{''}} + 5 y^{^{'}} + 4 y = 0, y (0) = 7, y^{^{'}} (0) = - 13

y^{^{'''}} - 3 y^{^{''}} + 5 y^{^{'}} + 9 y = 0

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

\frac{x ^{^{''}} - 3 x ^{^{'}}}{2} = 2 x - \frac{( x ^{^{'}} - 3 x )}{2}

What is the solution for y^{''}+10y^'+25y=0,y(0)=0,y^'(0)=-8 ?
The solution for y^{''}+10y^'+25y=0,y(0)=0,y^'(0)=-8 is y=-8e^{-5t}t