Integration factor of differential equation \(\frac{dy}{dx}\) + py = Q, where P and IQ are functions of x is
  • ∫e
  • \(_{e}\)∫pdx
  • \(_{e}\)-∫pdx
  • None of these
The radius of a circle is increasing at the rate of 0.4 cm/ s. The rate of increasing of its circumference is
  • 0.4 π cm/s
  • 0.8 π cm/s
  • 0.8 cm/s
  • None of these
The solution of \(\frac{dy}{dx}\) = 1 + x + y + xy is
  • x – y = k(1 + xy)
  • log (1 + y) = x + \(\frac{x^2}{2}\) + k
  • log (1 + x) + y + \(\frac{y^2}{2}\) = k
  • None of these
The degree of the differential equation
  • 1
  • 2
  • 3
  • not defined
The degree of differential equation[1 + (\(\frac{dy}{dx}\))²]= \(\frac{d^2y}{dx^2}\) is
  • 4
  • \(\frac{3}{2}\)
  • 2
  • not defined
The order and degree of the differential equation \(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))+ x= 0 respectvely, are
  • 2 and not defined
  • 2 and 2
  • 2 and 3
  • 3 and 3
If y = e
  • \(\frac{d^2y}{dx^2}\) + 2\(\frac{dy}{dx}\) = 0
  • \(\frac{d^2y}{dx^2}\) – 2\(\frac{dy}{dx}\) + 2y = 0
  • \(\frac{d^2y}{dx^2}\) + 2\(\frac{dy}{dx}\) + 2y = 0
  • \(\frac{d^2y}{dx^2}\) + 2y = 0
The differential equation for y = A cos αx + B sin αx where A and B are arbitary constants is
  • \(\frac{d^2y}{dx^2}\) – α²y = 0
  • \(\frac{d^2y}{dx^2}\) + α²y = 0
  • \(\frac{d^2y}{dx^2}\) + αy = 0
  • \(\frac{d^2y}{dx^2}\) – αy = 0
Solution of differential equation xdy – ydx = Q represents
  • a rectangular hyperbola
  • parabola whose vertex is at origin
  • straight line passing through origin
  • a circle whose centre is at origin
Integrating factor of the differential equation cos x \(\frac{dy}{dx}\) + y sin x = 1 is
  • cos x
  • tan x
  • sec x
  • sin x
Family r = Ax + A³ of curves is represented by the differential equation of degree
  • 1
  • 2
  • 3
  • 4
Integrating factor of \(\frac{xdy}{dx}\) – y = x – 3x is
  • x
  • log x
  • \(\frac{1}{2}\)
  • -x
Solution of \(\frac{dy}{dx}\) – y = 1 y(0) = 1 is given by
  • xy = -e
  • xy = -e
  • xy = -1
  • y = 2e
The number of solutions of \(\frac{dy}{dx}\) = \(\frac{y+1}{x-1}\) when y(1) = 2 is
  • none
  • one
  • two
  • infinite
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
Integrating factor of the differential equation
  • -x
  • \(\frac{x}{1+x^2}\)
  • \(\sqrt{1-x^2}\)
  • \(\frac{1}{2}\) log(1 – x²)
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
The differential equation y \(\frac{dy}{dx}\) + x = c represents
  • Family of hyperbolas
  • Family of parabolas
  • Family of ellipses
  • Family of circles
The degree of the differential equation \(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))³ + 6y = 0 is
  • 1
  • 2
  • 3
  • 5
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
0 h : 0 m : 1 s

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