What is the solution for (d^2y)/(dx^2)-12(dy)/(dx)+32y=0 ?

The solution for (d^2y)/(dx^2)-12(dy)/(dx)+32y=0 is y=c_{1}e^{8x}+c_{2}e^{4x}

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(d^2y)/(dx^2)-12(dy)/(dx)+32y=0

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 32 y = 0

y = c_{1} e^{8 x} + c_{2} e^{4 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 32 y = 0

Solve linear ODE:

y = c_{1} e^{8 x} + c_{2} e^{4 x}

y = c_{1} e^{8 x} + c_{2} e^{4 x}

y^{^{''}} + 4 y^{^{'}} + 12 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = \frac{1}{2}, y^{^{'}} (0) = \frac{1}{4}

10 y^{^{''''}} + 143 y^{^{''}} + 225 y = 0

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (- 1) = 3, y (- 1) = 9

y^{^{'''}} - 8 y^{^{''}} + 7 y^{^{'}} = 0

What is the solution for (d^2y)/(dx^2)-12(dy)/(dx)+32y=0 ?
The solution for (d^2y)/(dx^2)-12(dy)/(dx)+32y=0 is y=c_{1}e^{8x}+c_{2}e^{4x}