What is the solution for 3((d^2y)/(dx^2))+19((dy)/(dx))-14y=0 ?

The solution for 3((d^2y)/(dx^2))+19((dy)/(dx))-14y=0 is y=c_{1}e^{(2x)/3}+c_{2}e^{-7x}

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3((d^2y)/(dx^2))+19((dy)/(dx))-14y=0

3 (\frac{d ^{2} y}{d x ^{2}}) + 19 (\frac{d y}{d x}) - 14 y = 0

y = c_{1} e^{\frac{2 x}{3}} + c_{2} e^{- 7 x}

Solution steps

3 (\frac{d ^{2} y}{d x ^{2}}) + 19 (\frac{d y}{d x}) - 14 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{2 x}{3}} + c_{2} e^{- 7 x}

y = c_{1} e^{\frac{2 x}{3}} + c_{2} e^{- 7 x}

6 y^{^{'''}} + 2 y^{^{''}} = 0

(d^{3} + 8) y = 0

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

y^{^{''}} - 11 y^{^{'}} + 24 y = 0, y^{^{'}} (0) = 12

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

What is the solution for 3((d^2y)/(dx^2))+19((dy)/(dx))-14y=0 ?
The solution for 3((d^2y)/(dx^2))+19((dy)/(dx))-14y=0 is y=c_{1}e^{(2x)/3}+c_{2}e^{-7x}