Monday, 25 November 2019

MTH401-Differential Equations Quiz MCQs Lecture 1-7 Objective Questions | SUPERSTARWEBTECH


MTH401-Differential Equations Quiz  MCQS #Objective #Questions

1. Which of the following would be a general solution of the differential equaion: dy/dx = 4?
  • y = 4x+a
  • y = ax+4
  • y = 4x+4
  • y = ax+a
2. The order of the differential equation: d²y/dx²+5(dy/dx)³-3y = esin x is___.
  • 0
  • 1
  • 2
  • 3
3. ydx-y(sin x)dy = 0, is an example of ___ differential equation.
  • Exact
  • Non-Exact
  • Non-linear
  • Non-homogeneous
4. Which of the following substituton will transform the differential  equation: dy/dx = (x+y+1)/(x+2y+1), in to separable form?
  • y = v+x
  • y = vx
  • x = vy
  • x = X+h, y = Y+k
5. For the non-exact differential equation ydx-(y-3x-3)dy = 0, if (∂N/∂x-∂M/∂y)/M = 2/y, then the integrating factor is:
  • -1/y²
  • 1/y²
  • -y²
6. For f(x,y) = x²y-xy²,f(tx,ty) =...
  • f(x,y)
  • tf(x,y)
  • t²f(x,y)
  • t³f(x,y)
7. Which of the following is first order linear equation in unknown variable y?
  • x(dy/dx)+(sin x)y = cos x
  • y(dx/dy)+(sin y)x = cos y
  • y(dx/dy)+(sin y)x = cos x
  • y(dx/dy)+(sin x)x = cos y
8. Which of the following is the integrating factor for the 1st order linear differential equation: x(dy/dx)+y = f(x)
  • ex
  • lnx
  • x
  • 1/x
9. Which of the following are explicit solutions of the differential equation: dy/dx = -x/y
  • y = ±√(4+x)
  • y = ±√(-4+x²)
  • y = ±√(4-x²)
  • y = ±√(-4-x²)
10. A differential euation M(x,y)dx+N(x,y)dy = 0 is exact if there exists a multi-variable  function (x,y) such that ___
  • df(x,y) = (∂f/∂x)dx+(∂f/∂y)dy
  • ∫f(x,y)dx = ∫(∂f/∂x)dx+∫(∂f/∂y)dy
  • f(x,y) = (∂f/∂x)dx+(∂f/∂y)dy
  • f(x,y) = ∫(∂f/∂x)dx+∫(∂f/∂y)dy
11. The differential equation dx/dy+(1/y)x=2siny is first order linear in unknown___
  • variable x
  • variable y
  • multi-variables x and y
  • dy/dx
12. If the non-exact differntial equation M(x,y)dx+N(x,y)dy = 0 is homogeneous and xM(x,y)+yN(x,y) ≠ 0, then the integrating factor is:
  • (∂N/∂x-∂M/∂y)/M
  • (∂M/∂y-∂N/∂x)/N
  • 1/(xM-yN), xM-yN ≠ 0
  • 1/(xM+yN), xM+yN ≠ 0
13. The integrating factor for the first order linear differential equation: dy/dx+y cot x = sin² x is
  • sin x
  • cos x
  • e sin x
  • e cos x
14. Which of the following is an example of Homogeneous function?
  • f(x,y) = sin (1/x)
  • f(x,y) = sin (x/y)
  • f(x,y) = sin x
  • f(x,y) = sin xy
15. Which ofthe following would be a constantsolution of the separable differential equation: dy/dx = cos x sin y?
  • x = nπ,n∈ℤ
  • x = 2nπ,n∈ℤ
  • y = nπ,n∈ℤ
  • y = (n+1/2)π,n∈ℤ