What is the solution for y^{''}+10y^'+25y=0,y(0)=-3,y^'(0)=14 ?

The solution for y^{''}+10y^'+25y=0,y(0)=-3,y^'(0)=14 is y=-3e^{-5t}-e^{-5t}t

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y^{''}+10y^'+25y=0,y(0)=-3,y^'(0)=14

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = - 3, y^{^{'}} (0) = 14

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

Solution steps

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

Solve linear ODE:

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

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

f (x) = \frac{4}{x}, at x = \frac{1}{16}

\int (3 y - 2 y - 3) d y

\frac{d}{d x} ((8 x - 7)^{- 5})

x \to 0 lim (1 + x - 1)

y \to 0 lim (\frac{sin ( 5 y )}{7 y})

What is the solution for y^{''}+10y^'+25y=0,y(0)=-3,y^'(0)=14 ?
The solution for y^{''}+10y^'+25y=0,y(0)=-3,y^'(0)=14 is y=-3e^{-5t}-e^{-5t}t