What is the solution for y^{''}+10y^'+25y=0,y(0)=2,y^'(0)=-13 ?

The solution for y^{''}+10y^'+25y=0,y(0)=2,y^'(0)=-13 is y=2e^{-5t}-3e^{-5t}t

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y^{''}+10y^'+25y=0,y(0)=2,y^'(0)=-13

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = - 13

y = 2 e^{- 5 t} - 3 e^{- 5 t} t

Solution steps

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

Solve linear ODE:

y = 2 e^{- 5 t} - 3 e^{- 5 t} t

y = 2 e^{- 5 t} - 3 e^{- 5 t} t

\frac{3}{4} \frac{d ^{2} x}{d t ^{2}} + 72 x = 0, x (0) = \frac{1}{4}

y^{^{'''}} - 11 y^{^{''}} + 28 y^{^{'}} = 0

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

\frac{d ^{3} y}{d x ^{3}} - \frac{d ^{2} y}{d x ^{2}} = 0

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

What is the solution for y^{''}+10y^'+25y=0,y(0)=2,y^'(0)=-13 ?
The solution for y^{''}+10y^'+25y=0,y(0)=2,y^'(0)=-13 is y=2e^{-5t}-3e^{-5t}t