GATE ME 2021 Set 1 — Question 11
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33EasyFirst-Order EquationsDifferential EquationsEngineering Mathematics
Engineering Mathematics → Differential Equations → First-Order Equations
Last updated
Question
If satisfies the differential equationsubject to the condition , then is
Correct answer
(C) (π)/(3)
Solution
To find the value of , we begin by analyzing the given first-order ordinary differential equation:
Step 1: Simplify the Differential Equation
We recognize that the left-hand side of the equation is the exact derivative of the product with respect to using the product rule:Thus, the differential equation simplifies to:Step 2: Integrate both sides
Integrating both sides with respect to :where is the constant of integration.Step 3: Apply the boundary condition
We are given the condition . Substituting and into the integrated equation:Since :Step 4: Find the particular solution
Substituting back into the equation gives:Step 5: Calculate
Now, we evaluate at :Since :Conclusion
The value of is .Correct Option: CContinue 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 ME 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 Q11Domain is bounded by curve , ordinate , and axis. The value of…2026 Set 1 Q12Let be a scalar function. Then, is2026 Set 1 Q13The order and degree of the following differential equation are and , respectively.…2026 Set 1 Q14Newton-Raphson method for solving algebraic equations is based on2026 Set 1 Q15The exact solution of is represented as . If represents…