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Question 95Asked in BPSC TRE 1.0 (2023) Mathematics Class 11-12

The differential equation of y = eˣ(A cos x + B sin x) isy = eˣ(A cos x + B sin x) का अवकल समीकरण है

y = eˣ(A cos x + B sin x) का अवकल समीकरण है
  1. Ady/dx + 2y = 0dy/dx + 2y = 0
  2. Bd²y/dx² − 2 dy/dx + 2y = 0d²y/dx² − 2 dy/dx + 2y = 0
  3. Cd²y/dx² + 4y = 0d²y/dx² + 4y = 0
  4. DMore than one of the aboveउपर्युक्त में से एक से अधिक
  5. ENone of the aboveउपर्युक्त में से कोई नहीं
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Correct answer: (B) d²y/dx² − 2 dy/dx + 2y = 0d²y/dx² − 2 dy/dx + 2y = 0

Explanation

y = eˣ(A cos x + B sin x) is the general solution for auxiliary roots 1 ± i, whose auxiliary equation is m² − 2m + 2 = 0. So y″ − 2y′ + 2y = 0.y = eˣ(A cos x + B sin x) सहायक मूलों 1 ± i के लिए व्यापक हल है, जिनका सहायक समीकरण m² − 2m + 2 = 0 है। अतः y″ − 2y′ + 2y = 0।

From BPSC TRE 1.0 (2023) Mathematics Class 11-12 — Previous Year Paper

This is question 95 of BPSC TRE 1.0 (2023) Mathematics Class 11-12 — Previous Year Paper. See all questions of this paper with answers, or attempt the paper as a timed online test to get your score and all-India rank.