What is the solution for -2y^{''}+5y^'+10y=0 ?

The solution for -2y^{''}+5y^'+10y=0 is y=c_{1}e^{-((-5+sqrt(105))t)/4}+c_{2}e^{((5+sqrt(105))t)/4}

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-2y^{''}+5y^'+10y=0

- 2 y^{^{''}} + 5 y^{^{'}} + 10 y = 0

y = c_{1} e^{- \frac{( - 5 + 105 ) t}{4}} + c_{2} e^{\frac{( 5 + 105 ) t}{4}}

Solution steps

- 2 y^{''} (t) + 5 y^{'} (t) + 10 y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{( - 5 + 105 ) t}{4}} + c_{2} e^{\frac{( 5 + 105 ) t}{4}}

y = c_{1} e^{- \frac{( - 5 + 105 ) t}{4}} + c_{2} e^{\frac{( 5 + 105 ) t}{4}}

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = 2, y^{^{'}} (0) = 16

100 y^{^{''}} + 180 y^{^{'}} + 145 y = 0

y^{^{''}} + 4 y = 0, y (0) = 5, y^{^{'}} (0) = - 3

(D^{2} + 64)^{2} y = 0

y^{^{''}} = a^{2} y

What is the solution for -2y^{''}+5y^'+10y=0 ?
The solution for -2y^{''}+5y^'+10y=0 is y=c_{1}e^{-((-5+sqrt(105))t)/4}+c_{2}e^{((5+sqrt(105))t)/4}