Which of the following statements are TRUE?
A. Order of the differential equation is the order of highest differential appearing in the differential equation.
B. Degree of a differential equation is a real number.
C. Order of a differential equation is whole number.
D. Degree of a differential equation is the degree of the highest order derivative, when differential coefficients are free from radicals and fractions.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A, B, C and D
The order of a differential equation is the order of the highest order derivative in it. When the equation is a polynomial in its derivatives, its degree is the highest power of that highest order derivative.
So the order is always a positive integer, and the degree, when it is defined, is also a positive integer.
Checking the statements
(A) Order of the differential equation is the order of highest differential appearing in the differential equation. — Correct. This is the definition of order.
(B) Degree of a differential equation is a real number. — Correct. The degree is a positive integer, and every positive integer is a real number.
(C) Order of a differential equation is whole number. — Correct. The order is a positive integer, which is a whole number.
(D) Degree of a differential equation is the degree of the highest order derivative, when differential coefficients are free from radicals and fractions. — Correct. This is the definition of degree.