What is the solution for 6(d^2y)/(dx^2)+4(dy)/(dx)-2y=3x-2 ?

The solution for 6(d^2y)/(dx^2)+4(dy)/(dx)-2y=3x-2 is y=c_{1}e^{x/3}+c_{2}e^{-x}-(3x)/2-2

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6(d^2y)/(dx^2)+4(dy)/(dx)-2y=3x-2

6 \frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 2 y = 3 x - 2

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

Solution steps

6 \frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 2 y = 3 x - 2

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} + 5 y = t

y^{^{''}} - y^{^{'}} - 2 y = 4 x e^{3 x}

y^{^{''}} + 9 y = cos (t) \cdot H (t - π)

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

y^{''} - 25 y = x^{2} + x

What is the solution for 6(d^2y)/(dx^2)+4(dy)/(dx)-2y=3x-2 ?
The solution for 6(d^2y)/(dx^2)+4(dy)/(dx)-2y=3x-2 is y=c_{1}e^{x/3}+c_{2}e^{-x}-(3x)/2-2