CBSE  /  Class 12  /  Maths  /  Differential Equations

  • 1. 
    Solution of the differential equation tan y sec² x dx + tan x sec² y dy + 0 is . (a) tan x + tan y = k

  • 2. 
    Family r = Ax + A³ of curves is represented by the differential equation of degree

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  • 3. 
    Integrating factor of \(\frac{xdy}{dx}\) – y = x – 3x is

  • x
  • log x
  • \(\frac{1}{2}\)
  • -x

  • 4. 
    Solution of \(\frac{dy}{dx}\) – y = 1 y(0) = 1 is given by

  • xy = -e
  • xy = -e
  • xy = -1
  • y = 2e

  • 5. 
    The number of solutions of \(\frac{dy}{dx}\) = \(\frac{y+1}{x-1}\) when y(1) = 2 is

  • none
  • one
  • two
  • infinite

  • 6. 
    Which of the following is a second order differential equation?

  • (y’)² + x = y²
  • y’y” + y = sin x
  • y” + (y”)² + y = 0
  • y’ = y²

  • 7. 
    Integrating factor of the differential equation

  • -x
  • \(\frac{x}{1+x^2}\)
  • \(\sqrt{1-x^2}\)
  • \(\frac{1}{2}\) log(1 – x²)

  • 8. 
    tan x + tan y = c is the general solution of the differential equation

  • \(\frac{dy}{dx}\) = \(\frac{1+y^2}{1+x^2}\)
  • \(\frac{dy}{dx}\) = \(\frac{1+x^2}{1+y^2}\)
  • (1 + x²)dy + (1 + y²)dx = 0
  • (1 +x²2)dx+(1 + y²)dy = 0

  • 9. 
    The differential equation y \(\frac{dy}{dx}\) + x = c represents

  • Family of hyperbolas
  • Family of parabolas
  • Family of ellipses
  • Family of circles

  • 10. 
    The degree of the differential equation \(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))³ + 6y = 0 is

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