What is the solution for (xy+2x+y+2)dx+(x^2+2x)dy=0 ?

The solution for (xy+2x+y+2)dx+(x^2+2x)dy=0 is y=(c_{1})/(sqrt(x)\sqrt{x+2)}-2

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(xy+2x+y+2)dx+(x^2+2x)dy=0

(x y + 2 x + y + 2) d x + (x^{2} + 2 x) d y = 0

y = \frac{c _{1}}{x x + 2} - 2

Solution steps

(x y + 2 x + y + 2) d x + (x^{2} + 2 x) d y = 0

Solve separable ODE:

y = \frac{c _{1}}{x x + 2} - 2

y = \frac{c _{1}}{x x + 2} - 2

\int \frac{x + 1}{x ^{2} - 2 x + 1} d x

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

2 x y y^{^{'}} = x^{2} + 2 y^{2}

f (x) = 2 e^{4 x}

x^{2} + 8, - 2, 1

What is the solution for (xy+2x+y+2)dx+(x^2+2x)dy=0 ?
The solution for (xy+2x+y+2)dx+(x^2+2x)dy=0 is y=(c_{1})/(sqrt(x)\sqrt{x+2)}-2