Question:
The order and degree of the differential equation : \(\dfrac{d}{dx}(\sin y) = y^2\) respectively are
The order and degree of the differential equation : \(\dfrac{d}{dx}(\sin y) = y^2\) respectively are
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Apply the chain rule to get \(\cos y \cdot \frac{dy}{dx} = y^2\). Only a first derivative appears, with power 1.
Updated On: Oct 22, 2026
- 1, 1
- 2, 1
- 2, 2
- 1, 2
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
The order of a differential equation is the order of the highest derivative in it.
The degree is the power of that highest derivative, once the equation is a polynomial in its derivatives.
Step 2: Remove the outer derivative:
The left side is the derivative of \(\sin y\) with respect to \(x\). By the chain rule:
\[ \frac{d}{dx}(\sin y) = \cos y \cdot \frac{dy}{dx} \]
So the equation becomes:
\[ \cos y \cdot \frac{dy}{dx} = y^2 \]
Step 3: Find the order:
The only derivative present is \(\dfrac{dy}{dx}\), which is a first derivative. So the order is 1.
Step 4: Find the degree:
The equation is a polynomial in \(\dfrac{dy}{dx}\), and \(\dfrac{dy}{dx}\) appears only with power 1.
The term \(\cos y\) is a function of \(y\), not of the derivative, so it does not change the degree. So the degree is 1.
Step 5: Why the other options are wrong:
Options (B) and (C) say the order is 2, but there is no second derivative anywhere.
Option (D) says the degree is 2. The \(y^2\) on the right is a power of \(y\), not of the derivative.
Final Answer:
The order is 1 and the degree is 1, which is option (A). \[ \boxed{\text{Order} = 1, \ \text{Degree} = 1} \]
The order of a differential equation is the order of the highest derivative in it.
The degree is the power of that highest derivative, once the equation is a polynomial in its derivatives.
Step 2: Remove the outer derivative:
The left side is the derivative of \(\sin y\) with respect to \(x\). By the chain rule:
\[ \frac{d}{dx}(\sin y) = \cos y \cdot \frac{dy}{dx} \]
So the equation becomes:
\[ \cos y \cdot \frac{dy}{dx} = y^2 \]
Step 3: Find the order:
The only derivative present is \(\dfrac{dy}{dx}\), which is a first derivative. So the order is 1.
Step 4: Find the degree:
The equation is a polynomial in \(\dfrac{dy}{dx}\), and \(\dfrac{dy}{dx}\) appears only with power 1.
The term \(\cos y\) is a function of \(y\), not of the derivative, so it does not change the degree. So the degree is 1.
Step 5: Why the other options are wrong:
Options (B) and (C) say the order is 2, but there is no second derivative anywhere.
Option (D) says the degree is 2. The \(y^2\) on the right is a power of \(y\), not of the derivative.
Final Answer:
The order is 1 and the degree is 1, which is option (A). \[ \boxed{\text{Order} = 1, \ \text{Degree} = 1} \]
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