What is the solution for (x-a)ydx+xy^2dy=0 ?

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

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(x-a)ydx+xy^2dy=0

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

y = - 2 x + 2 a ln (x) + c_{1}, y = - - 2 x + 2 a ln (x) + c_{1}

Solution steps

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

Solve separable ODE:

y = - 2 x + 2 a ln (x) + c_{1}, y = - - 2 x + 2 a ln (x) + c_{1}

y = - 2 x + 2 a ln (x) + c_{1}, y = - - 2 x + 2 a ln (x) + c_{1}

\frac{d y}{d t} = \frac{3 t ^{2} + 4 t + 2}{2 y - 2}, y (0) = - 1

\frac{d x}{d y} = 2 y x^{2} + 2 y

y^{^{'}} = 5 y^{2} ln (x)

(t^{2} - 16 t + 15) y^{^{'}} = y

y^{^{'}} = (1 - 2 x) y^{2}, y (0) = \frac{- 1}{6}

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