What is the solution for 6(d^2y)/(dx^2)+(dy)/(dx)-y=0 ?

The solution for 6(d^2y)/(dx^2)+(dy)/(dx)-y=0 is y=c_{1}e^{x/3}+c_{2}e^{-x/2}

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6(d^2y)/(dx^2)+(dy)/(dx)-y=0

6 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - y = 0

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

Solution steps

6 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - y = 0

Solve linear ODE:

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

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

y^{^{''}} + 9 y = 0, y (0) = sin (3 x)

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

y^{^{'''}} - 3 y^{^{''}} + 4 y^{^{'}} - 12 y = 0

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

\frac{d ^{2}}{d θ ^{2}} (y (θ)) + y (θ) = 0

What is the solution for 6(d^2y)/(dx^2)+(dy)/(dx)-y=0 ?
The solution for 6(d^2y)/(dx^2)+(dy)/(dx)-y=0 is y=c_{1}e^{x/3}+c_{2}e^{-x/2}