Exercise
$\frac{dy}{dx}=\frac{2x^2\:+\:y^2}{2xy}$
Step-by-step Solution
Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=(2x^2+y^2)/(2xy). We can identify that the differential equation \frac{dy}{dx}=\frac{2x^2+y^2}{2xy} 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: y=ux. Expand and simplify. Integrate both sides of the differential equation, the left side with respect to u, and the right side with respect to x.
Solve the differential equation dy/dx=(2x^2+y^2)/(2xy)
Final answer to the exercise
$-2\ln\left|\frac{\sqrt{-y^2+2x^2}}{\sqrt{2}x}\right|=\ln\left|x\right|+C_0$