What is the solution for (d^2y)/(dx^2)-13(dy)/(dx)+12y=0 ?

The solution for (d^2y)/(dx^2)-13(dy)/(dx)+12y=0 is y=c_{1}e^{12x}+c_{2}e^x

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(d^2y)/(dx^2)-13(dy)/(dx)+12y=0

\frac{d ^{2} y}{d x ^{2}} - 13 \frac{d y}{d x} + 12 y = 0

y = c_{1} e^{12 x} + c_{2} e^{x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 13 \frac{d y}{d x} + 12 y = 0

Solve linear ODE:

y = c_{1} e^{12 x} + c_{2} e^{x}

y = c_{1} e^{12 x} + c_{2} e^{x}

\frac{3}{4} x^{^{''}} + 72 x = 0, x (0) = \frac{1}{3}, x^{^{'}} (0) = 0

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

y^{^{''}} + 81 y = 0, y (0) = 1, y^{^{'}} (0) = 7

2 y^{^{''}} + 4 y^{^{'}} + 6 y = 0

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d}{d x} (4) + 4 y = 0

What is the solution for (d^2y)/(dx^2)-13(dy)/(dx)+12y=0 ?
The solution for (d^2y)/(dx^2)-13(dy)/(dx)+12y=0 is y=c_{1}e^{12x}+c_{2}e^x