What is the solution for 3(d^2y)/(dx^2)-14(dy)/(dx)-5y=0 ?

The solution for 3(d^2y)/(dx^2)-14(dy)/(dx)-5y=0 is y=c_{1}e^{5x}+c_{2}e^{-x/3}

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3(d^2y)/(dx^2)-14(dy)/(dx)-5y=0

3 \frac{d ^{2} y}{d x ^{2}} - 14 \frac{d y}{d x} - 5 y = 0

y = c_{1} e^{5 x} + c_{2} e^{- \frac{x}{3}}

Solution steps

3 \frac{d ^{2} y}{d x ^{2}} - 14 \frac{d y}{d x} - 5 y = 0

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- \frac{x}{3}}

y = c_{1} e^{5 x} + c_{2} e^{- \frac{x}{3}}

9 y^{^{''}} - 16 y^{^{'}} = 0

y^{^{'}} + y^{^{''}} = y^{^{'''}}

y^{^{''}} + 8 y^{^{'}} + 15 y = 0, y (0) = 2, y (1) = 0

y^{^{''}} + 9 y^{^{'}} - 9 y = 0

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

What is the solution for 3(d^2y)/(dx^2)-14(dy)/(dx)-5y=0 ?
The solution for 3(d^2y)/(dx^2)-14(dy)/(dx)-5y=0 is y=c_{1}e^{5x}+c_{2}e^{-x/3}