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

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

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(dy)/(dx)+2xy=y+6x-3

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d}{d x} (\frac{2}{3 x})

y^{^{'''}} - 2 y^{^{'}} + y = 0

\int - 9 sin (3 x) d x

\int 12 x ln (3 x) d x

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