Consider the differential equation with the initial conditions given below. If y(x)
is the solution of the equation, the value of the slope,
dy
dx , at x = ln(2) is
________ (rounded off to three decimal places).
d2y
dx2 + 2 dy
dx + y = 0 with y|x=0 = 0 and dy
dx|
x=0
= 1
Official Answer Key:
0.0
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2026 Q.49)**
**1. Governing Concept & Syllabus Domain**:
This question pertains to **Linear Algebra & Differential Equations** under *Engineering Mathematics* (2 Marks, NAT).
**2. Analytical Calculation**:
- Substituting aerodynamic parameters into governing Linear Algebra & Differential Equations equation.
**3. Final Answer**:
Acceptable official numerical value is **0.0**.
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