Integrating factor of the differential equation \(\frac{dy}{dx}\) + y tan x – sec x = 0 is
  • cos x
  • sec x
  • e
  • e
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
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
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
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
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
Family y = Ax + A³ of curves will correspond to a differential equation of order
  • 3
  • 2
  • 1
  • not finite
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
The general solution of the differential equation \(\frac{dy}{dx}\) = e
  • y = ce
  • y = ce
  • y = (x + c)e
  • y = (c – x)e
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
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
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
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
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
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 = Ae + Be
  • y = A cos x + B sin x
  • None of the above
0 h : 0 m : 1 s

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