What is the solution for (d^2y)/(dx^2)-5((dy)/(dx))+6y=0 ?

The solution for (d^2y)/(dx^2)-5((dy)/(dx))+6y=0 is y=c_{1}e^{3x}+c_{2}e^{2x}

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(d^2y)/(dx^2)-5((dy)/(dx))+6y=0

\frac{d ^{2} y}{d x ^{2}} - 5 (\frac{d y}{d x}) + 6 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 5 (\frac{d y}{d x}) + 6 y = 0

Solve linear ODE:

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

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

y^{^{''}} + 10 y^{^{'}} + 16 y = 0, y (0) = 0, y^{^{'}} (0) = - 6

y^{^{''}} = \frac{y}{4}

y^{^{''}} - 4 y^{^{'}} + 8 y = 0, y^{^{'}} (0) = 2, y (0) = 0

y^{^{''}} = 6 y^{^{'}} - 8 y, y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} + 4 y^{1} - y = 0

What is the solution for (d^2y)/(dx^2)-5((dy)/(dx))+6y=0 ?
The solution for (d^2y)/(dx^2)-5((dy)/(dx))+6y=0 is y=c_{1}e^{3x}+c_{2}e^{2x}