GATE EC 2025 Set 1 — Question 32
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+1 / -0HardEuler-Cauchy EquationsDifferential EquationsEngineering MathematicsMaxima & MinimaCalculus
Engineering Mathematics → Calculus → Euler-Cauchy Equations
Last updated
Question
The function satisfieswhere and denote the first and second derivatives of , respectively.
Given and , the maximum value of over is _____ (rounded off to two decimal places).
Given and , the maximum value of over is _____ (rounded off to two decimal places).
Correct answer
0.25 to 0.25
Solution
The given differential equation is a Cauchy-Euler equation: .
Let . Substituting this into the equation gives the characteristic equation:
So, . The general solution is .
The derivative is .
Using the boundary conditions:
To find the maximum value on the interval , we set :
.
The maximum value is .
Let . Substituting this into the equation gives the characteristic equation:
So, . The general solution is .
The derivative is .
Using the boundary conditions:
1..
2..
Thus, the function is .To find the maximum value on the interval , we set :
.
The maximum value is .
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 Calculus
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 …