GATE BT 2024 • Q30
MCQ • 1 Mark
Section 1: Engineering Mathematics
Engineering Mathematics
Subtopic: Calculus, Linear Algebra & Probability
Question Statement:
The solution of the differential equation
dy
dx = y + e-x that satisfies y(0) = -
1
2 is
________.
Options:
-
(A) -
1
2 e-x
2
-
(B) -
1
2 ex
-
(C) -
1
2 e-x
-
(D) -
1
2 e
x
2
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2024 Q.30)**
**1. Governing Concept & Domain**:
This question evaluates **Engineering Mathematics** under *Section 1: Engineering Mathematics* (1 Mark, MCQ).
**2. Molecular / Bioprocess Mathematical Derivation**:
- Formulating the biological principles and kinetic expressions for Engineering Mathematics.
- Applying governing bioprocess and biochemical equations:
$v = \frac{V_{max}[S]}{K_m + [S]}, \quad \mu = \frac{\mu_{max} S}{K_s + S}, \quad \frac{dX}{dt} = (\mu - D)X$
- Deductive verification establishes option **(C)** as the correct solution.
**3. Final Answer**:
Correct Option is **(C)**.
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