What is the solution for 4(d^2y)/(dx^2)+32(dy)/(dx)+64y=0 ?

The solution for 4(d^2y)/(dx^2)+32(dy)/(dx)+64y=0 is y=c_{1}e^{-4x}+c_{2}xe^{-4x}

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4(d^2y)/(dx^2)+32(dy)/(dx)+64y=0

4 \frac{d ^{2} y}{d x ^{2}} + 32 \frac{d y}{d x} + 64 y = 0

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

Solution steps

4 \frac{d ^{2} y}{d x ^{2}} + 32 \frac{d y}{d x} + 64 y = 0

Solve linear ODE:

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

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

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (0) = 8, y^{^{'}} (0) = 9

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

y^{^{''}} + 4 y^{^{'}} - 32 y = 0, y (0) = a, y^{^{'}} (0) = - 40

77 y^{^{''''}} + 303 y^{^{''}} + 100 y = 0

x^{^{''}} + 25 x = 0, x (0) = 0.6, x^{^{'}} (0) = 1

What is the solution for 4(d^2y)/(dx^2)+32(dy)/(dx)+64y=0 ?
The solution for 4(d^2y)/(dx^2)+32(dy)/(dx)+64y=0 is y=c_{1}e^{-4x}+c_{2}xe^{-4x}