## Final Answer

## Step-by-step Solution

Problem to solve:

Specify the solving method

Factor the polynomial $y+xy$ by it's GCF: $y$

Learn how to solve differential equations problems step by step online.

$\frac{dx}{dy}=y\left(1+x\right)$

Learn how to solve differential equations problems step by step online. Solve the differential equation dx/dy=y+xy. Factor the polynomial y+xy by it's GCF: y. Group the terms of the differential equation. Move the terms of the x variable to the left side, and the terms of the y variable to the right side of the equality. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Solve the integral \int\frac{1}{1+x}dx and replace the result in the differential equation.