What is the solution for 9(d^2y)/(dx^2)-6(dy)/(dx)=0 ?

The solution for 9(d^2y)/(dx^2)-6(dy)/(dx)=0 is y=c_{1}e^{(2x)/3}+c_{2}

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} = 5 y^{^{'}} - 6 y

y^{^{''}} - c^{2} y = 0

2 y^{^{''}} - 2 y^{^{'}} - 2 y = 0

10 x^{^{''}} + 30 x^{^{'}} + 20 x = 0, x (0) = - 7, x^{^{'}} (0) = - 2

y^{^{''}} - 14 y^{^{'}} - 45 y = 0

What is the solution for 9(d^2y)/(dx^2)-6(dy)/(dx)=0 ?
The solution for 9(d^2y)/(dx^2)-6(dy)/(dx)=0 is y=c_{1}e^{(2x)/3}+c_{2}