What is the solution for y^{''}+10y^'+9y=0,y(0)=2,y^'(0)=0 ?

The solution for y^{''}+10y^'+9y=0,y(0)=2,y^'(0)=0 is y=(2+1/4)e^{-t}-1/4 e^{-9t}

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y^{''}+10y^'+9y=0,y(0)=2,y^'(0)=0

y^{^{''}} + 10 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y = (2 + \frac{1}{4}) e^{- t} - \frac{1}{4} e^{- 9 t}

Solution steps

y^{''} (t) + 10 y^{'} (t) + 9 y = 0

Solve linear ODE:

y = (2 + \frac{1}{4}) e^{- t} - \frac{1}{4} e^{- 9 t}

y = (2 + \frac{1}{4}) e^{- t} - \frac{1}{4} e^{- 9 t}

y^{^{''}} + 36 y = 0, y (0) = 0, y^{^{'}} (0) = 2

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} = 0

y^{^{'''}} - 7 y^{^{''}} = 0

\frac{4}{32} x^{^{''}} + x^{^{'}} + 2 x = 0, x (0) = - 1, x^{^{'}} (0) = 16

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} + 6 y = 0, y (1) = 3

What is the solution for y^{''}+10y^'+9y=0,y(0)=2,y^'(0)=0 ?
The solution for y^{''}+10y^'+9y=0,y(0)=2,y^'(0)=0 is y=(2+1/4)e^{-t}-1/4 e^{-9t}