Final answer to the problem
$\frac{1}{2}\ln\left|y\right|-\frac{1}{2}\ln\left|y+2\right|=\frac{1}{2}x^2+C_0$
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Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation y^'-xy^2=2xy. Rewrite the differential equation using Leibniz notation. We need to isolate the dependent variable y, we can do that by simultaneously subtracting -xy^2 from both sides of the equation. Multiply -1 times -1. Factor the polynomial 2xy+xy^2 by it's greatest common factor (GCF): xy.
Final answer to the problem
$\frac{1}{2}\ln\left|y\right|-\frac{1}{2}\ln\left|y+2\right|=\frac{1}{2}x^2+C_0$
