Exercise
$\frac{dy}{dx}\left(2yln\left(y\right)+y+x\right)=y$
Step-by-step Solution
Learn how to solve addition of numbers problems step by step online. Solve the differential equation dy/dx(2yln(y)+yx)=y. Rewrite the differential equation. We can identify that the differential equation \frac{dy}{dx}=\frac{y}{2y\ln\left(y\right)+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: x=uy. Expand and simplify.
Solve the differential equation dy/dx(2yln(y)+yx)=y
Final answer to the exercise
$\frac{x}{y}=\ln\left(y\right)^2+\ln\left(y\right)+C_0$