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^{^{''}} + 2 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 1

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

y^{^{''''}} - 38 y^{^{'''}} + 361 y^{^{''}} = 0

\frac{d ^{4} y}{d x ^{4}} + 5 \frac{d ^{2} y}{d x ^{2}} + 4 y = 0

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

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