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

Explanation

To solve the differential equation \( y e^{\frac{x}{y}} dx = (x e^{\frac{x}{y}} + y^2) dy \) where \( y \neq 0 \), we will follow these steps:

### Step 1: Rewrite the equation
We start with the given equation:
\[ y e^{\frac{x}{y}} dx = (x e^{\frac{x}{y}} + y^2) dy \]
We can rearrange this into a more manageable form by dividing both sides by \( y \):
...