Exercise
$\frac{dy}{dx}=\frac{-2xy}{y^2-x^2}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=(-2xy)/(y^2-x^2). We can identify that the differential equation \frac{dy}{dx}=\frac{-2xy}{y^2-x^2} is homogeneous, since it is written in the standard form \frac{dy}{dx}=\frac{M(x,y)}{N(x,y)}, where M(x,y) and N(x,y) are the partial derivatives of a two-variable function f(x,y) and both are homogeneous functions of the same degree. Use the substitution: x=uy. Expand and simplify. Integrate both sides of the differential equation, the left side with respect to u, and the right side with respect to y.
Solve the differential equation dy/dx=(-2xy)/(y^2-x^2)
Final answer to the exercise
$\ln\left|1+\frac{x^2}{y^2}\right|=-\ln\left|y\right|+C_0$