What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)-12=0 ?

The solution for (d^2y)/(dx^2)+4(dy)/(dx)-12=0 is y=c_{1}+c_{2}e^{-4x}+3x

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(d^2y)/(dx^2)+4(dy)/(dx)-12=0

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 12 = 0

y = c_{1} + c_{2} e^{- 4 x} + 3 x

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 12 = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- 4 x} + 3 x

y = c_{1} + c_{2} e^{- 4 x} + 3 x

y^{^{''}} + 4 y^{^{'}} + 5 y = \frac{2 e ^{2 x}}{sin ( x )}

y^{^{''}} + 9 y = t^{2} e^{3 t}

y^{^{''}} + 16 y = 8 cos (4 x) + 12 sin (4 x)

\frac{d ^{2} x}{d t ^{2}} + 9 x = 5 sin (3 t)

y^{^{''}} - y^{^{'}} - 2 y = (6 x^{2} + 8 x + 7) e^{x}

What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)-12=0 ?
The solution for (d^2y)/(dx^2)+4(dy)/(dx)-12=0 is y=c_{1}+c_{2}e^{-4x}+3x