What is the solution for (d^2y)/(dx^2)+12(dy)/(dx)+32y=160 ?

The solution for (d^2y)/(dx^2)+12(dy)/(dx)+32y=160 is y=c_{1}e^{-4x}+c_{2}e^{-8x}+5

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(d^2y)/(dx^2)+12(dy)/(dx)+32y=160

\frac{d ^{2} y}{d x ^{2}} + 12 \frac{d y}{d x} + 32 y = 160

y = c_{1} e^{- 4 x} + c_{2} e^{- 8 x} + 5

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 12 \frac{d y}{d x} + 32 y = 160

Solve linear ODE:

y = c_{1} e^{- 4 x} + c_{2} e^{- 8 x} + 5

y = c_{1} e^{- 4 x} + c_{2} e^{- 8 x} + 5

y^{^{''}} - 4 y^{^{'}} = 16 t + 36, y (- 2) = 2, y^{^{'}} (- 2) = - 1

\frac{d ^{2} y}{d x ^{2}} + a \frac{d y}{d x} = b

y^{^{''''}} - 5 y^{^{''}} + 4 y = 20 e^{3 x}

y^{^{''}} + 36 y = 12 tan (6 t)

(- 8 x^{^{''}} - 16 x^{^{'}} + 24) = 8 e^{2 t}

What is the solution for (d^2y)/(dx^2)+12(dy)/(dx)+32y=160 ?
The solution for (d^2y)/(dx^2)+12(dy)/(dx)+32y=160 is y=c_{1}e^{-4x}+c_{2}e^{-8x}+5