In reference to the differential equation: \( y''+y=(e)^{y'} \), which of the following statements are correct?
A. The order of the differential equation is 1.
B. The degree of the differential equation is 1.
C. The order of the differential equation is 2.
D. The degree of the differential equation is not defined.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → C and D only
The highest order derivative present is \( y'' \), and \( y' \) appears in the exponent of e. The degree is defined only when the equation is a polynomial in the derivatives, and \( e^{y'} \) is not a polynomial in \( y' \).
So the order is 2, and the degree is not defined.
Checking the statements
(A) The order of the differential equation is 1. — Incorrect. \( y'' \) is present, so the order is 2.
(B) The degree of the differential equation is 1. — Incorrect. Because of \( e^{y'} \), the degree is not defined.
(C) The order of the differential equation is 2. — Correct. The highest order derivative is \( y'' \).
(D) The degree of the differential equation is not defined. — Correct. \( e^{y'} \) is not a polynomial in \( y' \).
Tip: A derivative inside e, log, sin or cos makes the degree undefined, even when that derivative is not the highest one.
NCERT (2026-27 edition):
Degree of a Differential Equation
