What is the solution for (dy)/(dx)=(1+x)/(xy) ?

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

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(dy)/(dx)=(1+x)/(xy)

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = (y - 50)^{2}

\frac{d v}{d t} = 60 - \frac{7}{100} v, v = 0, t = 0

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

y^{^{'}} = (y - 1)^{2}, y (0) = 1.01

(x + 4) (2 y + 6) d y = x y^{2} d x

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