The number of arbitrary constants in the particular solution of a differential equation of order 4 and degree 3 is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0
The general solution of a differential equation of order n contains n arbitrary constants; here there would be 4.
A particular solution is obtained by giving definite values to all these constants, so it contains no arbitrary constant.
The degree, 3, plays no part in the count.
Why the other options are incorrect
Option (2) 1 — Incorrect. A particular solution has no arbitrary constant left.
Option (3) 3 — Incorrect. 3 is the degree, which does not decide the number of constants.
Option (4) 4 — Incorrect. 4 is the number of arbitrary constants in the general solution, equal to the order.
NCERT (2026-27 edition):
General and Particular Solutions of a Differential Equation
