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The degree of the differential equation y'''+(y')^2=0 is 2. 2. The general solution of a second order differential equation contains three arbitrary…

Single correct option

Consider the following statements:
1. The degree of the differential equation

y'''+(y')^2=0

2

.
2. The general solution of a second order differential equation contains three arbitrary constants.
Which of the statements given above is/are correct?

A. $1$ only
B. $2$ only
C. Both $1$ and $2$
D. Neither $1$ nor $2$

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Answer: (D) Neither $1$ nor $2$

For statement 1, the highest-order derivative is

y'''

and its power is

1

, so the degree is

1

, not

2

. For statement 2, the general solution of an

n

th order differential equation contains exactly

n

arbitrary constants, so a second order equation has two. Both statements are false.

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