Mathematics · Partial Differential Equations
Which of the following is the D'Alembert's solution of the one-dimensional wave equation utt = c2uxx subject to the initial conditions u(x,0) = f(x) and ut(x,0) = g(x)?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
Share:
- 1u(x,t) = 12[f(x + ct) + f(x - ct)] + 12c∫x - ctx + ct g(s) ds✓
- 2u(x,t) = 12[f(x + ct) + f(x - ct)] + 12c∫0x + ct g(s) ds
- 3u(x,t) = [f(x + ct) + f(x - ct)]
- 4u(x,t) = 12[f(x + ct) + f(x - ct)]
Correct answer
u(x,t) = 12[f(x + ct) + f(x - ct)] + 12c∫x - ctx + ct g(s) ds
Download Single Question PDF
Save this question and verified answer as a clean study sheet with live clickable link.
👥
Share with Friends & Study Groups
Challenge your peer aspirants on WhatsApp or Telegram to solve this question!
Online Test Series
Preparing for Mathematics?
Practice full-length Mathematics mock tests with real exam timers, instant score analysis, and all-India ranking.
Chapter Practice
Practice Partial Differential Equations MCQs →Want more practice questions on Partial Differential Equations?
Solve complete topic-wise tests with detailed solutions on GkGet.
Related Practice Questions
Recommended practice questions in Mathematics · Partial Differential Equations