Question

Assertion :The degree of the differential equation, $\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)+1=0$ is 1 Reason: By the degree of a differential equation, when it is a polynomial equation in derivatives, we mean the highest power (positive integral index) of the highest order derivative involved in the given differential equation.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is incorrect but Reason is correct
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is C Assertion is incorrect but Reason is correct

ASSERTION; The degree of a ordinary differential equation is defined as the highest power of the order in the differential equation when the differential equation is expressed as purely polynomial form.

here in the equation $\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)+1=0$

$\sin \left(\frac{dy}{dx}\right)$ is not an appropriate polynomial form but the whole equation is an trancendental equation for which we cannot define a degree of that differential equation.

REASON; It is true as the degree of a differential equation is defined only when it is expressed in a polynomial form.