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

Explanation

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

### Step 1: Rearranging the Equation
We start by rewriting the given equation in a more manageable form:
\[ y e^{\frac{x}{y}} dx = (x e^{\frac{x}{y}} + y^2) dy \]
Dividing both sides by \( dy \) gives:
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