Consider the partial differential equation
பమ
ப௫మ +
பమ
ப௬మ = 0 where x, y are real.
If f(x, y) = a(x)b(y), where a(x) and b(y) are real functions, which one of the
following statements can be true?
Options:
(A) a(x) is a periodic function and b(y) is a linear function
(B) both a(x) and b(y) are exponential functions
(C) a(x) is a periodic function and b(y) is an exponential function
(D) both a(x) and b(y) are periodic functions
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2022 Q.38)**
**1. Governing Concept & Syllabus Domain**:
This question pertains to **Linear Algebra & Differential Equations** under *Engineering Mathematics* (2 Marks, MCQ).
**2. Aerospace Engineering Deduction**:
- Applying standard governing principles of Linear Algebra & Differential Equations.
- Option **(A)** matches the analytical derivation and official criteria.
**3. Final Answer**:
Correct Option is **(A)**.
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