Question:
The order and degree of the differential equation \(e^{\frac{dy}{dx}}+\frac{dy}{dx}=x\) is
The order and degree of the differential equation \(e^{\frac{dy}{dx}}+\frac{dy}{dx}=x\) is
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Order is the highest derivative present; degree exists only if the equation is a polynomial in the derivatives.
Updated On: Nov 12, 2026
- order = 1 and degree = 1
- order = 1 and degree = 2
- order = 1 and degree = not defined
- order = not defined and degree = 1
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
Order is the highest order derivative. Degree is the power of that derivative, defined only if the equation is a polynomial in derivatives.
Step 2: Find the order
The highest derivative is \(\frac{dy}{dx}\), so the order is 1.
Step 3: Check the degree
The term \(e^{dy/dx}\) cannot be written as a polynomial in \(\frac{dy}{dx}\) (it is an infinite series).
Step 4: Conclude
So the degree is not defined.
Final Answer:
The order is 1 and the degree is not defined. \[ \boxed{\text{(C) }\text{order = 1 and degree = not defined}} \]
Order is the highest order derivative. Degree is the power of that derivative, defined only if the equation is a polynomial in derivatives.
Step 2: Find the order
The highest derivative is \(\frac{dy}{dx}\), so the order is 1.
Step 3: Check the degree
The term \(e^{dy/dx}\) cannot be written as a polynomial in \(\frac{dy}{dx}\) (it is an infinite series).
Step 4: Conclude
So the degree is not defined.
Final Answer:
The order is 1 and the degree is not defined. \[ \boxed{\text{(C) }\text{order = 1 and degree = not defined}} \]
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