GATE CE 2023 Set 1 — Question 30
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+1 / -0MediumFirst-Order Linear EquationsOrdinary Differential EquationsEngineering MathematicsInitial Value Problems
Engineering Mathematics → Ordinary Differential Equations → First-Order Linear Equations
Last updated
Question
In the differential equation , is a positive constant. If at , and at , the value of is _______________(rounded off to three decimal places).
Correct answer
0.445 to 0.447
Solution
The given differential equation is:This is a separable differential equation:Integrating both sides:Using the first boundary condition: at
So, the equation becomes:Using the second boundary condition: at
Rounding off to three decimal places, .
So, the equation becomes:Using the second boundary condition: at
Rounding off to three decimal places, .
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 CE 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.