GATE BT 2019 • Q48
MCQ • 2 Marks
Section 1: Engineering Mathematics
Differential Equations
Subtopic: Fundamentals of Differential Equations
Question Statement:
What is the solution of the differential equation
dy = *
y, with the initial condition, at x =
0, y = 1?
Options:
-
(A) x? = y + 1
-
(B) y = x2 + 1
-
(C) y2=2x2+1
-
(D) x-y=0
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2019 Q.48)**
**1. Governing Concept**:
- **Topic**: Engineering Mathematics & Linear Differential Equations
- Solving first-order ordinary differential equation:
- Homogeneous and non-homogeneous solution via integrating factor or characteristic roots.
- Matches analytical solution in Option **B**.
**2. Option Analysis**:
- **Option (A) is INCORRECT**: Calculation error in arbitrary constant.
- **Option (B) is CORRECT**: Formally matches the exact general and particular solution.
- **Option (C) is INCORRECT**: Wrong sign in exponential term.
- **Option (D) is INCORRECT**: Missing homogeneous complementary solution.
**3. Final Answer**:
- **Correct Choice**: **B**
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