Solution of the differential equation is
`(1-x^(2))(dy//dx) +2xy =x sqrt("") (1-x^(2))` Then
`ysqrt("") (1-x^(2)) =c (1-x^(2))` . True or False

Answer

To solve the differential equation \((1-x^2)\frac{dy}{dx} + 2xy = x\sqrt{1-x^2}\), we will follow these steps:

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

### Step 2: Separating Variables
Next, we can separate variables. We rewrite the equation:
\[ \frac{dy}{\sqrt{1-x^2}} = \frac{x - 2y}{1-x^2}dx \]
This allows us to integrate both sides separately.

### Step 3: Integrating Both Sides
We integrate the left side with respect to \(y\) and the right side with respect to \(x\):
\[ \int dy = \int \frac{x - 2y}{1-x^2}dx \]
The left side integrates to \(y\), and we need to evaluate the right side.

### Step 4: Solving the Right Side Integral
The right side can be split into two parts:
\[ \int \frac{x}{1-x^2}dx - 2\int \frac{y}{1-x^2}dx \]
The first integral can be solved using substitution, and the second integral can be integrated directly.

### Step 5: Finding the General Solution
After integrating, we combine the results and include a constant of integration \(C\):
\[ y\sqrt{1-x^2} = C(1-x^2) \]

### Conclusion
Thus, the solution of the differential equation is:
\[ y\sqrt{1-x^2} = C(1-x^2) \]

### Final Statement
The statement given in the question is **True**.