What is the solution for y^{''}+10y^'+25y=0,y(-1)=6,y^'(-1)=4 ?

The solution for y^{''}+10y^'+25y=0,y(-1)=6,y^'(-1)=4 is y=40e^{-5t-5}+34e^{-5t-5}t

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y^{''}+10y^'+25y=0,y(-1)=6,y^'(-1)=4

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (- 1) = 6, y^{^{'}} (- 1) = 4

y = 40 e^{- 5 t - 5} + 34 e^{- 5 t - 5} t

Solution steps

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

Solve linear ODE:

y = 40 e^{- 5 t - 5} + 34 e^{- 5 t - 5} t

y = 40 e^{- 5 t - 5} + 34 e^{- 5 t - 5} t

What is the solution for y^{''}+10y^'+25y=0,y(-1)=6,y^'(-1)=4 ?
The solution for y^{''}+10y^'+25y=0,y(-1)=6,y^'(-1)=4 is y=40e^{-5t-5}+34e^{-5t-5}t