What is the solution for y^{''}+10y^'+25y=0,y(0)=-4,y^'(0)=16 ?

The solution for y^{''}+10y^'+25y=0,y(0)=-4,y^'(0)=16 is y=-4e^{-5t}-4e^{-5t}t

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y^{''}+10y^'+25y=0,y(0)=-4,y^'(0)=16

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = - 4, y^{^{'}} (0) = 16

y = - 4 e^{- 5 t} - 4 e^{- 5 t} t

Solution steps

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

Solve linear ODE:

y = - 4 e^{- 5 t} - 4 e^{- 5 t} t

y = - 4 e^{- 5 t} - 4 e^{- 5 t} t

What is the solution for y^{''}+10y^'+25y=0,y(0)=-4,y^'(0)=16 ?
The solution for y^{''}+10y^'+25y=0,y(0)=-4,y^'(0)=16 is y=-4e^{-5t}-4e^{-5t}t