Consider the differential equation
d2௬
d௫మ - 2
d௬
d௫ + y = 0.
The boundary conditions are y = 0 and
ௗ௬
ௗ௫ = 1 at x = 0.
Then the value of y at x = 1/2 is
Options:
(A) 0
(B) √e
(C) √e
2
(D) ටe
2
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2022 Q.37)**
**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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