What is the solution for (x+y+1)dx-(y-x+3)dy=0 ?

The solution for (x+y+1)dx-(y-x+3)dy=0 is y=-3+x-sqrt(2x^2-4x+9-c_{1)},y=-3+x+sqrt(2x^2-4x+9-c_{1)}

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(x+y+1)dx-(y-x+3)dy=0

(x + y + 1) d x - (y - x + 3) d y = 0

y = - 3 + x - 2 x^{2} - 4 x + 9 - c_{1}, y = - 3 + x + 2 x^{2} - 4 x + 9 - c_{1}

Solution steps

(x + y + 1) d x - (y - x + 3) d y = 0

Solve exact ODE:

y = - 3 + x - 2 x^{2} - 4 x + 9 - c_{1}, y = - 3 + x + 2 x^{2} - 4 x + 9 - c_{1}

y = - 3 + x - 2 x^{2} - 4 x + 9 - c_{1}, y = - 3 + x + 2 x^{2} - 4 x + 9 - c_{1}

x \to - 1 lim (7 ∣ x + 1 ∣ - 4)

\int e^{2 x} d x

\int \frac{x ( 6 x ^{2} + 6 )}{x ^{2} + 1} d x

\frac{d}{d x} (- 2 sin (x) - sin (2 x))

\frac{d}{d x} ((x + 1) e^{a r c t a n (x)})

What is the solution for (x+y+1)dx-(y-x+3)dy=0 ?
The solution for (x+y+1)dx-(y-x+3)dy=0 is y=-3+x-sqrt(2x^2-4x+9-c_{1)},y=-3+x+sqrt(2x^2-4x+9-c_{1)}