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

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

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

linear

\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}

- 2 y^{^{''}} - 2 \cdot π^{2} y = 0

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 4, y^{^{'}} (0) = 1

\frac{d ^{2} x}{d t ^{2}} - 2 \frac{d x}{d t} - 15 x = 0

\frac{d ^{2} y}{d t ^{2}} - 20 \frac{d y}{d t} + 100 y = 0

y^{^{''}} - 10 y^{^{'}} - 171 y = 0, y (0) = 9, y^{^{'}} (0) = 3

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