What is the solution for y^{''}+10y^'+25y=0,y(0)=2,y^'(0)=-9 ?

The solution for y^{''}+10y^'+25y=0,y(0)=2,y^'(0)=-9 is y=2e^{-5t}+e^{-5t}t

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y^{''}+10y^'+25y=0,y(0)=2,y^'(0)=-9

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = - 9

y = 2 e^{- 5 t} + e^{- 5 t} t

Solution steps

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

Solve linear ODE:

y = 2 e^{- 5 t} + e^{- 5 t} t

y = 2 e^{- 5 t} + e^{- 5 t} t

y^{^{''}} - y^{^{'}} - 12 y = 0, y (0) = 2, y^{^{'}} (0) = - 3

5 y^{^{'}} + 6 y^{^{''}} = 0

y^{^{''}} - 400 y = 0

y^{^{''}} + (1 + a) y = 0

y^{^{''}} - 8 y^{^{'}} + 15 y = 0, y (0) = 1, y^{^{'}} (0) = 1

What is the solution for y^{''}+10y^'+25y=0,y(0)=2,y^'(0)=-9 ?
The solution for y^{''}+10y^'+25y=0,y(0)=2,y^'(0)=-9 is y=2e^{-5t}+e^{-5t}t