Q.3) The degree of the differential equation $$1+\left(\frac{d y}{d x}\right)^2=x$$ is $$\_\_\_\_$$ .

Answer: 2

The degree of a differential equation is the power (exponent) of the highest-order derivative

In the given equation, $$1+\left(\frac{d y}{d x}\right)^2=x$$ :
– The highest order derivative is the first derivative, $$\frac{d y}{d x}$$.
– This term is raised to the power of 2.
– The equation is a polynomial in its derivatives.

Therefore, the degree of the differential equation is $$\mathbf{2}$$.