What is the solution for y^{''}+10y^'+25y=0,y(0)=-1,y^'(0)=7 ?

The solution for y^{''}+10y^'+25y=0,y(0)=-1,y^'(0)=7 is y=-e^{-5t}+2e^{-5t}t

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y^{''}+10y^'+25y=0,y(0)=-1,y^'(0)=7

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = - 1, y^{^{'}} (0) = 7

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 10 y + 16 y = 0

8 \frac{d ^{2} y}{d t ^{2}} + 12 \frac{d y}{d t} + 5 y = 0

\frac{d ^{2} y}{d t ^{2}} - 18 \frac{d y}{d t} + 81 y = 0

y^{^{'''}} + 4 y^{^{''}} - 25 y^{^{'}} - 28 y = 0

y^{^{''}} + 3 y^{^{'}} + 6 \cdot y = 0, y (0) = 0, y^{^{'}} (0) = 1

What is the solution for y^{''}+10y^'+25y=0,y(0)=-1,y^'(0)=7 ?
The solution for y^{''}+10y^'+25y=0,y(0)=-1,y^'(0)=7 is y=-e^{-5t}+2e^{-5t}t