What is the solution for y^{''}+7y^'+10y=0,y(0)=11,y^'(0)=-49 ?

The solution for y^{''}+7y^'+10y=0,y(0)=11,y^'(0)=-49 is y=2e^{-2t}+9e^{-5t}

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y^{''}+7y^'+10y=0,y(0)=11,y^'(0)=-49

y^{^{''}} + 7 y^{^{'}} + 10 y = 0, y (0) = 11, y^{^{'}} (0) = - 49

y = 2 e^{- 2 t} + 9 e^{- 5 t}

Solution steps

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

Solve linear ODE:

y = 2 e^{- 2 t} + 9 e^{- 5 t}

y = 2 e^{- 2 t} + 9 e^{- 5 t}

4000 y^{^{''}} - 9 y^{^{'}} = 0

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3 \frac{d ^{2} y}{d x ^{2}} - 14 \frac{d y}{d x} - 5 y = 0

9 y^{^{''}} - 16 y^{^{'}} = 0

What is the solution for y^{''}+7y^'+10y=0,y(0)=11,y^'(0)=-49 ?
The solution for y^{''}+7y^'+10y=0,y(0)=11,y^'(0)=-49 is y=2e^{-2t}+9e^{-5t}