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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 8 y^{^{'}} + 16 y = 2 e^{4 x}

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{x} cos (x)

y^{^{''}} + 4 y^{^{'}} + 13 y = 5 cos (2 t)

x^{^{''}} - 6 x^{^{'}} + 10 x = 30 t

y^{^{''}} - y^{^{'}} - 12 y = (x + 1) e^{x}

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