What is the solution for xy(y+2)dx-(y+1)dy=0 ?

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

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xy(y+2)dx-(y+1)dy=0

x y (y + 2) d x - (y + 1) d y = 0

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

Solution steps

x y (y + 2) d x - (y + 1) d y = 0

Solve separable ODE:

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

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

y^{^{'}} csc (t) = \frac{- y ^{17}}{16}

7 y y^{^{'}} = 3 x

y^{^{'}} = 6 x^{2} (1 - 7 e^{- y})

e^{x + y} sin (x) d x + (2 y + 1) e^{- y^{2}} d y = 0

\frac{d y}{d x} = \frac{4 x y}{( ln ( y ) ) ^{2}}

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