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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

755 x^{^{''}} + 2 x^{^{'}} + 10 x = 0

(D^{(6)} - 4 D^{(4)} + 4 D^{(2)}) y = 0

y^{^{''}} + 12 y^{^{'}} + 27 y = 0, y (0) = 12, y^{^{'}} (0) = - 84

y^{^{'''}} - 3 y^{^{'}} = 0

y^{^{''}} + 10 y^{^{'}} = - 21 y

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