Formation Of De
The differential equation formed by eliminating arbitrary constants from y = Ae^x + Be^(-x) is
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About This Question
- Subject
- mathematics
- Chapter
- differential equations
- Topic
- formation of de
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
d²y/dx² - y = 0
- Identify Number of Constants: There are 2 constants (A,B), so we need two differentiations.
- First Derivative:
- y′=Aex−Be−x
- Second Derivative:
- y′′=Aex+Be−x
- Eliminate Constants: Notice that the right-hand side of y′′ is identical to the original function y.
- y′′=y⟹y′′−y=0.
- Standard Notation: dx2d2y−y=0.
This medium difficulty mathematics question is from the chapter differential equations, covering the topic of formation of de. It appeared in the 2025 exam.
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