Question

By eliminating the arbitrary constants from \[ y = (a + b)\sin(x + c) - de^{x + te^t} \] the differential equation obtained is of order:

• A. 6
• B. 4
• C. 3
• D. 5

Hint:

The number of arbitrary constants in a function determines the order of the resulting differential equation after elimination.

Answer 1

The Correct Option is C

There are three arbitrary constants: \( a, b, c \) in the term \( (a + b)\sin(x + c) \), and \( d \) in the exponential term. However, note that \( a + b \) appears as a single term and not individually. So, effectively, we are eliminating 3 constants: \( a + b \), \( c \), and \( d \). Hence, the order of the differential equation obtained is 3.