What is the solution for y^{''}+10y^'+25y=0,y(0)=-1,y^'(0)=0 ?

The solution for y^{''}+10y^'+25y=0,y(0)=-1,y^'(0)=0 is y=-e^{-5t}-5e^{-5t}t

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y^{''}+10y^'+25y=0,y(0)=-1,y^'(0)=0

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = - 1, y^{^{'}} (0) = 0

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 5

9 y^{^{''}} - 5 y^{^{'}} - 4 y = 0

y^{^{''}} + 25 y^{^{'}} + 2500 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + y^{^{'}} + 16 y = 0

y^{^{'''}} - 8 y^{^{'}} = 0

What is the solution for y^{''}+10y^'+25y=0,y(0)=-1,y^'(0)=0 ?
The solution for y^{''}+10y^'+25y=0,y(0)=-1,y^'(0)=0 is y=-e^{-5t}-5e^{-5t}t