Exercise
$x\:\cdot\frac{dy}{dx}=4x\:+\:y$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation xdy/dx=4x+y. Rewrite the differential equation. We can identify that the differential equation \frac{dy}{dx}=\frac{4x+y}{x} 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.
Solve the differential equation xdy/dx=4x+y
Final answer to the exercise
$y=\left(4\ln\left(x\right)+C_0\right)x$