Solve the differential equation `y e^(x/y)dx=(x e^(x/y)+y^2siny)dy(y!=0)`

Explanation

To solve the differential equation \( y e^{\frac{x}{y}} dx = \left( x e^{\frac{x}{y}} + y^2 \sin y \right) dy \), we will follow these steps:

### Step 1: Rearranging the Equation
We start with the given equation:
\[ y e^{\frac{x}{y}} dx = \left( x e^{\frac{x}{y}} + y^2 \sin y \right) dy \]
We can rearrange this equation to isolate \( dx \) and \( dy \):
...