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

The solution for y^{''}+7y^'+10y=0,y(0)=1,y^'(0)=0 is y=(1+2/3)e^{-2t}-2/3 e^{-5t}

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

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

y = (1 + \frac{2}{3}) e^{- 2 t} - \frac{2}{3} e^{- 5 t}

Solution steps

y^{''} (t) + 7 y^{'} (t) + 10 y = 0

Solve linear ODE:

y = (1 + \frac{2}{3}) e^{- 2 t} - \frac{2}{3} e^{- 5 t}

y = (1 + \frac{2}{3}) e^{- 2 t} - \frac{2}{3} e^{- 5 t}

x \to 0 lim (\frac{2}{3 + 4 ^{\frac{1}{x}}})

y = x^{3} + 1, (- 1, 2)

\frac{\partial}{\partial x} (y x - ln (x^{3} y + 6 x))

\frac{\partial}{\partial x} ((x - y) e^{y + 2 x^{2}})

What is the solution for y^{''}+7y^'+10y=0,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+7y^'+10y=0,y(0)=1,y^'(0)=0 is y=(1+2/3)e^{-2t}-2/3 e^{-5t}