What is the solution for (d^2y)/(dx^2)-9(dy)/(dx)+18y=0 ?

The solution for (d^2y)/(dx^2)-9(dy)/(dx)+18y=0 is y=c_{1}e^{6x}+c_{2}e^{3x}

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(d^2y)/(dx^2)-9(dy)/(dx)+18y=0

\frac{d ^{2} y}{d x ^{2}} - 9 \frac{d y}{d x} + 18 y = 0

y = c_{1} e^{6 x} + c_{2} e^{3 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 9 \frac{d y}{d x} + 18 y = 0

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{3 x}

y = c_{1} e^{6 x} + c_{2} e^{3 x}

y^{^{''}} + 5 y^{^{'}} + 4 y = 0, y^{^{'}} (0) = 1, y (0) = 1

y^{^{''}} + 1000 y^{^{'}} + 250000 y = 0

y^{^{''}} + 9 y = 0, y (0) = 5, y^{^{'}} (0) = - 7

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

2 y = 3 y^{^{''}}

What is the solution for (d^2y)/(dx^2)-9(dy)/(dx)+18y=0 ?
The solution for (d^2y)/(dx^2)-9(dy)/(dx)+18y=0 is y=c_{1}e^{6x}+c_{2}e^{3x}