Exercise
$x\:sin\left(\frac{y}{x}\right)\left(y\right)^'=ysin\left(\frac{y}{x}\right)+x$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation xsin(y/x)y^'=ysin(y/x)+x. Rewrite the differential equation using Leibniz notation. Rewrite the differential equation. We can identify that the differential equation \frac{dy}{dx}=\frac{y\sin\left(\frac{y}{x}\right)+x}{x\sin\left(\frac{y}{x}\right)} 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.
Solve the differential equation xsin(y/x)y^'=ysin(y/x)+x
Final answer to the exercise
$y=x\arccos\left(-\ln\left(x\right)+C_0\right)$