Solve the differential equation `x^2dy+y(x+y)dx=0,` given that `y=1\ w h e n\ x=1.`

Explanation

To solve the differential equation \( x^2 dy + y(x+y)dx = 0 \) with the initial condition \( y = 1 \) when \( x = 1 \), we can follow these steps:

### Step 1: Rearranging the Equation
We start by rearranging the given equation:
\[ x^2 dy = -y(x+y)dx \]
Now, we can express \(\frac{dy}{dx}\):
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