Discussion
The two partial differential equations \(f(x, y, z, p, q) = 0\) and \(g(x, y, z, p, q) = 0\) are said to be compatible if :
Answer: C
Two first-order equations are compatible if they have common solution.
That is the definition used in the theory of first-order PDEs (Sneddon): \(f(x, y, z, p, q) = 0\) and \(g(x, y, z, p, q) = 0\) are compatible when they have solutions in common, in practice a one-parameter family; it is not required that every solution of one also solve the other. This is the idea behind Charpit's method, which looks for a second equation compatible with the given one.
The first two options demand that one solution set contain the other, which is far stronger and is not the definition. The last option is the opposite of compatibility.
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