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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

∣ X^{2} - 1 ∣

\int e^{t y} (- 4 y - 1) d y

(4 - \frac{1}{2 x ^{2}})^{- 1}

f (x) = x^{2} - 3 x - 4, (2, - 6)

\frac{d}{d x} (4 x^{3} + 4 x)

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