What is the solution for 10y^{''}+9y^'+2y=0,y(0)=0,y^'(0)=5 ?

The solution for 10y^{''}+9y^'+2y=0,y(0)=0,y^'(0)=5 is y=50e^{-(2t)/5}-50e^{-t/2}

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10y^{''}+9y^'+2y=0,y(0)=0,y^'(0)=5

10 y^{^{''}} + 9 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 5

y = 50 e^{- \frac{2 t}{5}} - 50 e^{- \frac{t}{2}}

Solution steps

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

Solve linear ODE:

y = 50 e^{- \frac{2 t}{5}} - 50 e^{- \frac{t}{2}}

y = 50 e^{- \frac{2 t}{5}} - 50 e^{- \frac{t}{2}}

What is the solution for 10y^{''}+9y^'+2y=0,y(0)=0,y^'(0)=5 ?
The solution for 10y^{''}+9y^'+2y=0,y(0)=0,y^'(0)=5 is y=50e^{-(2t)/5}-50e^{-t/2}