What is the solution for y^{''}+13y^'+30y=0,y(0)=1,y^'(0)=0 ?

The solution for y^{''}+13y^'+30y=0,y(0)=1,y^'(0)=0 is y=(1+3/7)e^{-3t}-3/7 e^{-10t}

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y^{''}+13y^'+30y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 13 y^{^{'}} + 30 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = (1 + \frac{3}{7}) e^{- 3 t} - \frac{3}{7} e^{- 10 t}

Solution steps

y^{''} (t) + 13 y^{'} (t) + 30 y = 0

Solve linear ODE:

y = (1 + \frac{3}{7}) e^{- 3 t} - \frac{3}{7} e^{- 10 t}

y = (1 + \frac{3}{7}) e^{- 3 t} - \frac{3}{7} e^{- 10 t}

x \to \infty lim (\frac{5}{x} - 2)

\int (3 x + 5)^{3} d x

f (x) = x^{4} sin (4 x)

x \to 2 lim (x (2))

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What is the solution for y^{''}+13y^'+30y=0,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+13y^'+30y=0,y(0)=1,y^'(0)=0 is y=(1+3/7)e^{-3t}-3/7 e^{-10t}