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}

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}