Exercise
$\frac{dy}{dx}=xy+xy^2$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=xy+xy^2. Factor the polynomial xy+xy^2 by it's greatest common factor (GCF): xy. 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}\frac{1}{1+y}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 differential equation dy/dx=xy+xy^2
Final answer to the exercise
$\ln\left|y\right|-\ln\left|y+1\right|=\frac{1}{2}x^2+C_0$