What is the solution for y^{''}+9y^'+20y=0,y(0)=1,y^'(0)=0 ?

The solution for y^{''}+9y^'+20y=0,y(0)=1,y^'(0)=0 is y=5e^{-4t}-4e^{-5t}

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y^{''}+9y^'+20y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 9 y^{^{'}} + 20 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = 5 e^{- 4 t} - 4 e^{- 5 t}

Solution steps

y^{''} (t) + 9 y^{'} (t) + 20 y = 0

Solve linear ODE:

y = 5 e^{- 4 t} - 4 e^{- 5 t}

y = 5 e^{- 4 t} - 4 e^{- 5 t}

\frac{d y}{d x} = \frac{3 x}{e ^{y}}

\frac{d y}{d x} = \frac{- y ^{2}}{1 + y ^{2}} e^{(- x)}, y (0) = 1

\int \frac{x ^{2} - 5 x + 16}{x ( x - 2 ) ^{2}} d x

y = 12 x, y = x^{2}

n = 0 \sum \infty (2)^{n}

What is the solution for y^{''}+9y^'+20y=0,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+9y^'+20y=0,y(0)=1,y^'(0)=0 is y=5e^{-4t}-4e^{-5t}