Order of differential equation \( xy \frac{d^2y}{dx^2} + x \left( \frac{dy}{dx} \right)^2 - y \frac{dy}{dx} = 0 \) is 2.
Order of differential equation \( xy \frac{d^2y}{dx^2} + x \left( \frac{dy}{dx} \right)^2 - y \frac{dy}{dx} = 0 \) is 2.
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Solution and Explanation
Step 1: Identifying the order of the differential equation.
The given equation is:
\[
xy \frac{d^2y}{dx^2} + x \left( \frac{dy}{dx} \right)^2 - y \frac{dy}{dx} = 0.
\]
The highest derivative of \( y \) with respect to \( x \) in this equation is \( \frac{d^2y}{dx^2} \), which is the second derivative.
Step 2: Conclusion.
Since the highest derivative is the second derivative, the order of the differential equation is 2. Hence, the statement is true.
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