Linear Second Order Differential Equations MCQ

Test your knowledge with important Linear Second Order Differential Equations MCQ and their applications. These MCQs are beneficial for competitive exams too. Explore 30+ more Linear Second Order Differential Equations MCQs on Bissoy. Bissoy App

• What will be the value of C if C the constant of the coefficient of the solution of the given equation (D + 1)2y = 0 given y = 2 loge 2 when x = loge 2 and y = (4/3) loge3 when x = loge3?
  ক

  2

  খ

  -2

  গ

  -4

  ঘ

  4
• If, A and B are arbitrary constants then what will be the differential equation of y = Ax + B/x?
  ক

  x2 d2 y/dx2 – xdy/dx + y = 0

  খ

  x2 d2 y/dx2 + xdy/dx + y = 0

  গ

  x2 d2 y/dx2 + xdy/dx – y = 0

  ঘ

  x2 d2 y/dx2 – xdy/dx – y = 0
• Which of the following is the valid differential equation x = a cos(αt + β)?
  ক

  d2x/dt2 – αx = 0

  খ

  d2x/dt2 + αx = 0

  গ

  d2x/dt2 – α2x = 0

  ঘ

  d2x/dt2 + α2x = 0
• What is the solution of the given equation (D + 1)2y = 0 given y = 2 loge 2 when x = loge 2 and y = (4/3) loge3 when x = loge3?
  ক

  y = 4xe-x

  খ

  y = 4xex

  গ

  y = -4xe-x

  ঘ

  y = -4xex
• What will be the general solution of the differential equation d2y/dx2 = e2x(12 cos3x – 5 sin3x)? (here, A and B are integration constant)
  ক

  y = ex sin3x + Ax + B

  খ

  y = e2x sin3x + Ax + B

  গ

  y = e2x sin3x + A

  ঘ

  Data inadequate
• What will be the required solution of d2y/dx2 – 3dy/dx + 4y = 0?
  ক

  Ae-4x + Be-x

  খ

  Ae4x – Be-x

  গ

  Ae4x + Be-x

  ঘ

  Ae4x + Bex
• If y = t(x) be a differentiable function ᵾ x € R, then which of the following is always true?
  ক

  d2y/dx2 – (dy/dx)3 = 0

  খ

  d2y/dx2 + (dy/dx)3 d2x/dy2 = 0

  গ

  d2y/dx2 – (dx/dy)3 = 0

  ঘ

  d2y/dx2 + (dy/dx)3 = 0
• What is the differential equation of all parabolas whose directrices are parallel to the x-axis?
  ক

  d3x/dy3 = 0

  খ

  d3y/(dx3 + d2y/dx2) = 0

  গ

  d3y/dx3 = 0

  ঘ

  d2y/dx2 = 0
• What is thedifferential equation whose solution represents the family y = ae3x + bex?
  ক

  d2y/dx2 – 3dy/dx + 4y = 0

  খ

  d2y/dx2 – 4dy/dx + 3y = 0

  গ

  d2y/dx2 + 4dy/dx + 3y = 0

  ঘ

  d2y/dx2 – 4dy/dx – 3y = 0
• Which one of the following is correct if we differentiate the equation xy = aex + be-x two times?
  ক

  x(d2y/ dx) + 2(dy/dx) = xy

  খ

  x(d2y/ dx) – 2(dy/dx) = xy

  গ

  3x(d2y/ dx) + 2(dy/dx) = xy

  ঘ

  x(d2y/ dx) + 2(dy/dx) = 2xy