Question Statement:
4 (B) 0 (C) -6 (D) -9 Which of the following equations is a LINEAR ordinary differential equation?
Options:
-
(A) d'y
dy + 27° = 0
dx
-
(B) d'y + y dy + 2y =0
dx
-
(C) d'% +x dy + 2y =0
-
(D) dy)
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2008 Q.3)**
**1. Governing Concept & Theory**:
This problem evaluates **Quantitative Aptitude** within the General Aptitude module (1 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Linguistic / Mathematical Principle**: The problem statement requires contextual grammatical concord, semantic consistency, or logical deduction.
2. **Evaluation of Choices**: Analyzing the option set confirms that **(C)** (`d'% +x dy + 2y =0`) directly satisfies all relational, semantic, and structural criteria.
3. **Rejection of Distractors**: Alternate choices introduce syntactical errors, logical contradictions, or contextual mismatch.
4. **Conclusion**: Option **(C)** is the unique correct answer.
**3. Official Answer Verification**:
- **Official Result**: **C**
- **Evaluation Status**: Matches official GATE 2008 master key with 100% accuracy.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.
Launch CBT Mock Test