CBSE  /  Class 12  /  Maths  /  Differential Equations

  • 1. 
    The solution of the equation (2y – 1) dx-(2x + 3)dy = 0 is

  • \(\frac{2x-1}{2y+3}\) = k
  • \(\frac{2y+1}{2x-3}\) = k
  • \(\frac{2x+3}{2y-1}\) = k
  • \(\frac{2x-1}{2y-1}\) = k

  • 2. 
    The differential equation for which y = a cos x + b sin x is a solution is

  • \(\frac{d^2y}{dx^2}\) + y = 0
  • \(\frac{d^2y}{dx^2}\) – y = 0
  • \(\frac{d^2y}{dx^2}\) + (a + b)y = 0
  • \(\frac{d^2y}{dx^2}\) + (a – b)y = 0

  • 3. 
    The solution of \(\frac{dy}{dx}\) + y = e, y (0) = 0 is

  • y = e
  • y = xe
  • y = xe+ 1
  • y = xe

  • 4. 
    The order and degree of the differential equation(\(\frac{d^2y}{dx^3}\))² – 3\(\frac{d^2y}{dx^2}\) +2(\(\frac{dy}{dx}\))= y are

  • 1, 4
  • 3, 4
  • 2, 4
  • 3, 2

  • 5. 
    The order and degree of the differential equation [1 + (\(\frac{dy}{dx}\))²] = \(\frac{d^2y}{dx^2}\) are

  • 1, \(\frac{3}{2}\)
  • 2, 3
  • 2, 1
  • 3, 4

  • 6. 
    The differential equation of the family of curves y² = 4a (x + a) is

  • y² = 4\(\frac{dy}{dx}\) (x + \(\frac{dy}{dx}\))
  • 2y\(\frac{dy}{dx}\) = 4a
  • y\(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))² = 0
  • 2x\(\frac{dy}{dx}\) + y(\(\frac{dy}{dx}\))² – y

  • 7. 
    Which of the following is the general solution of \(\frac{d^2y}{dx^2}\) – 2\(\frac{dy}{dx}\) + y = 0

  • y = (Ax + B)e
  • y = (Ax + B)e
  • y = Ae + Be
  • y = A cos x + B sin x
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