GATE CE 2026 Set 2 — Question 46
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0EasyFirst-Order Linear EquationsOrdinary Differential EquationsEngineering Mathematics
Engineering Mathematics → Ordinary Differential Equations → First-Order Linear Equations
Last updated
Question
Consider differential equation with the condition as at .
The value of at is ______ (rounded off to two decimal places).
The value of at is ______ (rounded off to two decimal places).
Correct answer
0.37 to 0.42
Solution
The given differential equation is a first-order linear differential equation of the form , where and .Step 1: Find the integrating factor (IF).Step 2: Write the general solution.To solve the integral , let , then .So, the general solution is:Step 3: Apply the initial condition .Step 4: Find the particular solution.Step 5: Calculate at .Rounding to two decimal places, we get 0.39.
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.