Exercise
$\frac{dy}{dx}=y-y^2$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=y-y^2. 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 differential equation dy/dx=y-y^2
Final answer to the exercise
$y=\frac{e^x}{C_1+e^x}$