What is the solution for (d^2y)/(dx^2)-16(dy)/(dx)+64y=0 ?

The solution for (d^2y)/(dx^2)-16(dy)/(dx)+64y=0 is y=c_{1}e^{8x}+c_{2}xe^{8x}

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(d^2y)/(dx^2)-16(dy)/(dx)+64y=0

\frac{d ^{2} y}{d x ^{2}} - 16 \frac{d y}{d x} + 64 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 16 \frac{d y}{d x} + 64 y = 0

Solve linear ODE:

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

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

y^{^{''}} + 10 y^{^{'}} + 5 y = 0

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

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

y^{^{''}} + 8 y^{^{'}} + 15 y = 0, y (0) = 0, y^{^{'}} (0) = 1

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

What is the solution for (d^2y)/(dx^2)-16(dy)/(dx)+64y=0 ?
The solution for (d^2y)/(dx^2)-16(dy)/(dx)+64y=0 is y=c_{1}e^{8x}+c_{2}xe^{8x}