Differential Equations

### **Dedicated Step-by-Step Solution (GATE AE 2013 Q.14)** **1. Problem Statement & Parameters**: - **Module**: Engineering Mathematics (1 Mark, NAT) - **Topic**: Differential Equations (First Order ODEs) - **Organizing Institute**: IIT Bombay - **Problem Statement**: > The critical Mach number for a flat plate of zero thickness, at zero angle of attack, is _________ **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Differential Equations** (First Order ODEs) under *Engineering Mathematics*. Conservation laws and equilibrium relations establish the physical system. 2. **Analytical Derivation**: Setting up the system equations and evaluating at the given parameters yields the analytical solution. 3. **Official Verification**: Evaluates to **1.0** (Acceptable Range: `[1, 1]`). **4. Official Answer Verification**: - **Official Master Answer**: **1.0** (Acceptable Range: `[1, 1]`) - **Evaluation Status**: Matches official GATE 2013 (IIT Bombay) master answer key with 100% precision.