What is the solution for (d^2y)/(dx^2)+8(dy)/(dx)+16=0 ?

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

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(d^2y)/(dx^2)+8(dy)/(dx)+16=0

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 16 = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 16 = 0

Solve linear ODE:

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

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

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} - 2 y = 6 e x + 10 cos (x)

y^{^{''}} = 2 y + 22 cot^{3} (x), y (0) = 11 cot (x)

2 y^{^{''}} + 18 y + 5 = 0, y (0) = 0, y^{^{'}} (0) = 0

y, (d^{3} + 4 d) y = 2 t + t^{2}

y^{^{''}} - 9 y = x

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