What is the solution for 10y^{''}+9y^'+2y=0,y(0)=0,y^'(0)=3 ?

The solution for 10y^{''}+9y^'+2y=0,y(0)=0,y^'(0)=3 is y=30e^{-(2t)/5}-30e^{-t/2}

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10y^{''}+9y^'+2y=0,y(0)=0,y^'(0)=3

10 y^{^{''}} + 9 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 3

y = 30 e^{- \frac{2 t}{5}} - 30 e^{- \frac{t}{2}}

Solution steps

10 y^{''} (t) + 9 y^{'} (t) + 2 y = 0

Solve linear ODE:

y = 30 e^{- \frac{2 t}{5}} - 30 e^{- \frac{t}{2}}

y = 30 e^{- \frac{2 t}{5}} - 30 e^{- \frac{t}{2}}

(1) y^{^{''}} + (8) y^{^{'}} - (7) y = 0

\frac{d ^{8} y}{d x ^{8}} + 8 \frac{d ^{4} y}{d x ^{4}} + 16 y = 0

4 y^{^{''}} + 4 y^{^{'}} + 17 y = 0, y (0) = - 1, y^{^{'}} (0) = - 2

x^{^{''}} + \frac{x}{a} = 0

9 y^{^{''}} - 2 y^{^{'}} - 7 y = 0

What is the solution for 10y^{''}+9y^'+2y=0,y(0)=0,y^'(0)=3 ?
The solution for 10y^{''}+9y^'+2y=0,y(0)=0,y^'(0)=3 is y=30e^{-(2t)/5}-30e^{-t/2}