CBSE  /  Class 12  /  Maths  /  Differential Equations

  • 1. 
    The solution of \(\frac{dy}{dx}\) + y = e, y (0) = 0 is

  • y = e(x – 1)
  • y = xe
  • y = xe+ 1
  • y = (x + 1 )e

  • 2. 
    Integrating factor of the differential equation \(\frac{dy}{dx}\) + y tan x – sec x = 0 is

  • cos x
  • sec x
  • e
  • e

  • 3. 
    The solution of the differential equation \(\frac{dy}{dx}\) = \(\frac{1+y^2}{1+x^2}\)

  • y = tan x
  • y – x = k(1 + xy)
  • x = tan y
  • tan (xy) = k

  • 4. 
    The integrating factor of the differential equation \(\frac{dy}{dx}\) + y = \(\frac{1+y}{x}\) is

  • \(\frac{x}{e^x}\)
  • \(\frac{e^x}{x}\)
  • xe
  • e

  • 5. 
    y = ae+ be satisfies which of the following differential equation?

  • \(\frac{dy}{dx}\) + my = 0
  • \(\frac{dy}{dx}\) – my = 0
  • \(\frac{d^2y}{dx^2}\) – m²y = 0
  • \(\frac{d^2y}{dx^2}\) +m²y = 0

  • 6. 
    The solution of the differential equation cos x sin y dx + sin x cos y dy = 0 is

  • \(\frac{sin x}{sin y}\) = c
  • sin x sin y = c
  • sin x + sin y = z
  • cos x cos y = c

  • 7. 
    The differential equation of the family of cuves x² + y² – 2ay = 0, where a is arbitrary constant is

  • (x² – y²)\(\frac{dy}{dx}\) = 2xy
  • 2 (x² + y²)\(\frac{dy}{dx}\) = xy
  • 2(x² – y²)\(\frac{dy}{dx}\) = xy
  • (x² + y²) \(\frac{dy}{dx}\) = 2xy

  • 8. 
    Family y = Ax + A³ of curves will correspond to a differential equation of order

  • 3
  • 2
  • 1
  • not finite

  • 9. 
    The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is

  • an ellipse
  • parabola
  • circle
  • rectangular hyperbola

  • 10. 
    The general solution of the differential equation \(\frac{dy}{dx}\) = e

  • y = ce
  • y = ce
  • y = (x + c)e
  • y = (c – x)e
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