What is the solution for u^2ydy+uy^2du+ydy-2uydy=0 ?

The solution for u^2ydy+uy^2du+ydy-2uydy=0 is y=(e^{\frac{1+c_{1}u-c_{1})/(u-1)}}{u-1}

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u^2ydy+uy^2du+ydy-2uydy=0

u^{2} y d y + u y^{2} d u + y d y - 2 u y d y = 0

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

Solution steps

u^{2} y d y + u y^{2} d u + y d y - 2 u y d y = 0

Solve separable ODE:

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

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

\frac{d P}{d t} = 2 Pt, P (1) = 7

(y + y \cdot cos (x) y) d x + (x + x \cdot cos (x) y) d y = 0

x^{^{'}} = \frac{- 1}{t} \cdot x - \frac{1}{t}

\frac{d y}{d x} = \frac{x ^{2} - 7}{y ^{2}}, y (0) = 5

y^{2} d y = \frac{2 x + 1}{2 y} d x

What is the solution for u^2ydy+uy^2du+ydy-2uydy=0 ?
The solution for u^2ydy+uy^2du+ydy-2uydy=0 is y=(e^{\frac{1+c_{1}u-c_{1})/(u-1)}}{u-1}