Final answer to the problem
Step-by-step Solution
Specify the solving method
Solve the product $y\left(1-y\right)$
Any expression multiplied by $1$ is equal to itself
When multiplying two powers that have the same base ($y$), you can add the exponents
Solve the product $y\left(1-y\right)$
When multiplying two powers that have the same base ($y$), you can add the exponents
Group the terms of the differential equation. Move the terms of the $y$ variable to the left side, and the terms of the $x$ variable to the right side of the equality
Simplify the expression $\frac{1}{y-y^2}dy$
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 $\int\frac{1}{y\left(1-y\right)}dy$ and replace the result in the differential equation
Solve the integral $\int1dx$ and replace the result in the differential equation