What is the solution for (uy+y)(udy+ydu)-uydy=0 ?

The solution for (uy+y)(udy+ydu)-uydy=0 is y(u)=(e^{(1+c_{1}u)/u})/(u)

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(uy+y)(udy+ydu)-uydy=0

(u y + y) (u d y + y d u) - u y d y = 0

y (u) = \frac{e ^{\frac{1 + c _{1} u}{u}}}{u}

Solution steps

(u y (u) + y (u)) (u d y (u) + y (u) d u) - u y (u) d y (u) = 0

Solve separable ODE:

y (u) = \frac{e ^{\frac{1 + c _{1} u}{u}}}{u}

y (u) = \frac{e ^{\frac{1 + c _{1} u}{u}}}{u}

\frac{d y}{d x} = - \frac{5}{3} x^{9} y^{8}

\frac{d x}{d t} = a - b x^{2}

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

\frac{d V}{d t} = 60 - \frac{3}{100} V

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

What is the solution for (uy+y)(udy+ydu)-uydy=0 ?
The solution for (uy+y)(udy+ydu)-uydy=0 is y(u)=(e^{(1+c_{1}u)/u})/(u)