GATE EE 2016 Set 1 — Question 14
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33MediumHigher-Order Linear ODEsDifferential EquationsEngineering MathematicsInitial & Boundary Value Problems
Engineering Mathematics → Differential Equations → Higher-Order Linear ODEs
Last updated
Question
A function , such that and , is a solution of the differential equation . Then is
Correct answer
(B) 5e⁻²
Solution
The given differential equation is .
The characteristic equation is , which gives , so .
The general solution is .
Using the boundary conditions:
To find :
.
The characteristic equation is , which gives , so .
The general solution is .
Using the boundary conditions:
1..
2..
Thus, the specific solution is . To find :
.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE EE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Differential Equations
2026 Set 1 Q14Consider the following differential equation:…2026 Set 1 Q30Two matrices and have a common eigenvalue , and the same corresponding…2026 Set 1 Q32Given that , the integral…2026 Set 1 Q35 is an skew-symmetric matrix with real-valued entries, and is an…2026 Set 1 Q36A time-limited waveform is specified as follows:…