Exercise
$\left(x^2+2\:x\:y\right)y'+2y^2=-3xy$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation (x^2+2xy)y^'+2y^2=-3xy. Rewrite the differential equation using Leibniz notation. Rewrite the differential equation in standard form. We need to isolate the dependent variable y, we can do that by simultaneously subtracting \frac{2y^2}{x^2+2xy} from both sides of the equation. Multiplying the fraction by -1.
Solve the differential equation (x^2+2xy)y^'+2y^2=-3xy
Final answer to the exercise
$-\frac{1}{4}\ln\left(\frac{y}{x}\right)-\frac{1}{4}\ln\left(\frac{y}{x}+1\right)=\ln\left(x\right)+C_0$