Degree of the differential equation: a((dy)/(dx))² + b(dx)/(dy) = c, is 3

Assertion: Degree of the differential equation: $a\left(\frac{dy}{dx}\right)^2 + b\frac{dx}{dy} = c$, is 3

Reason: If each term involving derivatives of a differential equation is a polynomial (or can be expressed as polynomial) then highest exponent of the highest order derivative is called the degree of the differential equation.

(a)Both Assertion and Reason are true and Reason is the correct explanation for Assertion.
(b)Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.
(c)Assertion is true and Reason is false.
(d)Assertion is false and Reason is true.

Answer

Correct option: (a)

Answer: (a) Both Assertion and Reason are true and Reason is the correct explanation for Assertion. $a\left(\frac{dy}{dx}\right)^2 + b\frac{dx}{dy} = c$ with $\frac{dx}{dy} = \frac{1}{p}$, $p = \frac{dy}{dx}$: multiplying by $p$ gives $a p^3 - c p + b = 0$, a polynomial in $\frac{dy}{dx}$ whose highest power is 3. So the degree is 3 (Assertion true), and this uses exactly the definition in the Reason (true).