GATE EC 2020 Set 1 — Question 37
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67EasyFirst-Order Linear EquationsDifferential EquationsEngineering Mathematics
Engineering Mathematics → Differential Equations → First-Order Linear Equations
Last updated
Question
Which one of the following options contains two solutions of the differential equation ?
Correct answer
(A) ln y - 1 = 0.5x² + C and y = 1
Solution
The given differential equation is .
Using separation of variables:
Integrating both sides:
Additionally, by inspection, is a constant solution because if , then and , satisfying the equation.
Therefore, the two solutions are and .
Using separation of variables:
Integrating both sides:
Additionally, by inspection, is a constant solution because if , then and , satisfying the equation.
Therefore, the two solutions are and .
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 EC 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 Q11Consider the differential equation , with…2026 Set 1 Q12A surface is given by and and are unit…2026 Set 1 Q23The relation between the input current () and the output voltage () of a circuit is governed…2026 Set 1 Q26Consider the matrix . Which…2026 Set 1 Q36Consider the two series, and , where …