Discussion
The elimination of arbitrary constants \(c_{1}, c_{2}, c_{3}\) and \(c_{4}\) from \(y = (c_{1} + c_{2})\) sin \((x + c_{3}) - c_{4}e^{x}\) gives a differential equation of order
Answer: C
The order is 3.
The order equals the number of independent arbitrary constants. \(c_{1}\) and \(c_{2}\) appear only as the sum \(c_{1} + c_{2}\), which is a single constant A. So the family is \(y = A\sin(x + c_{3}) - c_{4}e^{x}\).
That leaves three independent constants, A, \(c_{3}\) and \(c_{4}\), so eliminating them needs three differentiations and gives a third-order equation. Counting the four letters gives 4, which overlooks that \(c_{1}\) and \(c_{2}\) cannot be separated.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development