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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{x d y}{d x} = 6 y

x \to 7 lim (x^{2} - 49)

\int \frac{8 + x ^{2}}{x} d x

\int_{- 2}^{2} (x^{2} + 1) d x

2 y^{^{''}} + 7 y^{^{'}} + 3 y = 0

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