Question Statement:
If ()ut is a unit step function, the solution of the differential equation
2
2 ()dxmk x u tdt += in
Laplace domain is
Options:
-
(A) 2
1
()sm s k+
-
(B) 2
1
ms k+
-
(C) 2
s
ms k+
-
(D) 22
1
()sm s k +
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2012 Q.12)**
**1. Governing Concept & Syllabus Domain**:
This question pertains to **Linear Algebra & Differential Equations** under *Engineering Mathematics* (1 Mark, MCQ).
**2. Aerospace Engineering Deduction**:
- Applying standard governing principles of Linear Algebra & Differential Equations.
- Option **(A)** matches the analytical derivation and official criteria.
**3. Final Answer**:
Correct Option is **(A)**.
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