Learn how to solve problems step by step online. Solve the differential equation dy/dx=(-x+4y)/(6x+y). We can identify that the differential equation \frac{dy}{dx}=\frac{-x+4y}{6x+y} 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=(-x+4y)/(6x+y)