What is the solution for y^{''}+3y^'+2y=0,y(0)=1,y^'(0)=0 ?

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

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y^{''}+3y^'+2y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 3 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = 0

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

Solution steps

y^{''} (t) + 3 y^{'} (t) + 2 y = 0

Solve linear ODE:

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

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

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x \to 0 lim (\frac{( 6 ^{x} - 4 ^{x} )}{x})

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