What is the solution for 2y^{''}+23y^'-12y=0 ?

The solution for 2y^{''}+23y^'-12y=0 is y=c_{1}e^{t/2}+c_{2}e^{-12t}

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2y^{''}+23y^'-12y=0

2 y^{^{''}} + 23 y^{^{'}} - 12 y = 0

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{- 12 t}

Solution steps

2 y^{''} (t) + 23 y^{'} (t) - 12 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{- 12 t}

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{- 12 t}

a \frac{d ^{2} y}{d x ^{2}} - y b^{2} = 0

4 y^{^{''}} + 28 y^{^{'}} + 49 y = 0, y (0) = 1, y^{^{'}} (0) = - 6

14 y^{^{''}} + 5 y^{^{'}} - 6 y = 0

y^{^{''}} - 24 y^{^{'}} + 10 y = 0

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

What is the solution for 2y^{''}+23y^'-12y=0 ?
The solution for 2y^{''}+23y^'-12y=0 is y=c_{1}e^{t/2}+c_{2}e^{-12t}