What is the solution for y^{''}+5y^'+6y=0,y(0)=1,y^'(0)=0 ?

The solution for y^{''}+5y^'+6y=0,y(0)=1,y^'(0)=0 is y=3e^{-2t}-2e^{-3t}

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y^{''}+5y^'+6y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = 3 e^{- 2 t} - 2 e^{- 3 t}

Solution steps

y^{''} (t) + 5 y^{'} (t) + 6 y = 0

Solve linear ODE:

y = 3 e^{- 2 t} - 2 e^{- 3 t}

y = 3 e^{- 2 t} - 2 e^{- 3 t}

\frac{\partial}{\partial x} (x^{y^{x}})

\int \frac{1}{x ^{2} + 64} d x

y = 2 x^{3} - x^{2} + 2

\int \frac{e ^{x^{n}}}{x ^{1 - n}} d x

h \to 0 lim (\frac{5 e ^{x} - 5 e ^{x + h}}{3 h})

What is the solution for y^{''}+5y^'+6y=0,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+5y^'+6y=0,y(0)=1,y^'(0)=0 is y=3e^{-2t}-2e^{-3t}