Differential Equation

1

If (2 + sin x) dy/dx + (y + 1)cos x = 0 and y(0) = 1, then y(π/2) is equal to

  1. 1/3
  2. -2/3
  3. -1/3
  4. 4/3
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2

The differential equation which represents the family of curves y = c1ec2x where c1 and c2 are arbitrary constants, is

  1. yy'' = y'
  2. y'' = y'y
  3. y' = y2
  4. yy'' = (y')2
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3

Let y(x) be the solution of the differential equation (x log x)(dy/dx) + y = 2x log(x), (x≥1). Then y(e) is equal to

  1. 0
  2. 2e
  3. e
  4. 2
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4

The solution of the equation d2y/dx2 = e-2x is

  1. e-2x/4
  2. 1/4 * e-2x + cx2 + d
  3. e-2x/4 + cx + d
  4. 1/4 * e-4x + cx + d
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5

The order and degree of the differential equation (1 + 3dy/dx)2/3 = 4d3y/dx3 are

  1. (3, 3)
  2. (3, 1)
  3. (1, 2)
  4. (1, 2/3)
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