Mathematics - Differential Equations

Question - 1

The order and degree of the differential equation, \({ \left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 2 }+\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } \)= 4, are respectively

  • A 2, 3
  • B 3, 2
  • C 3, 1
  • D NONE OF THESE

Question - 2

The order and degree of the differential equation \(\frac { { d }^{ 2 }s }{ d{ r }^{ 2 } } +3{ \left( \frac { ds }{ dt } \right) }^{ 2 }\) = t \(\log { \left( \frac { { d }^{ 2 }s }{ d{ r }^{ 2 } } \right) } \), respectively are

  • A 2, 2
  • B 2, 1
  • C 2, 3
  • D NONE OF THESE

Question - 3

The degree of the differential equation \({ \left( \frac { { d }^{ 3 }y }{ { dx }^{ 3 } } \right) }^{ 4/3 }+3\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +\frac { dy }{ dx } \) + 1 = 0, is

  • A 3
  • B 4
  • C 2
  • D NOT DEFINED

Question - 4

The degree and the order of the differential equation \(\frac { { d }^{ 2 }y }{ x{ d }^{ 2 } } +\frac { 2 }{ \left( \frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } \right) } \)+ 4y = 0 are

  • A 2, 2
  • B 4, 2
  • C 2, 4
  • D 2, 1

Question - 5

The differential equation representing the family of curves y2 = 2c(x + \(\sqrt { c } \)), where c is a positive parameter, is of order

  • A 1
  • B 2
  • C 3
  • D 4

Question - 6

A solution of the differential equation \({ \left( \frac { dy }{ dx } \right) }^{ 2 }-x\frac { dy }{ dx } \)+ y = 0, is

  • A y = 2
  • B y = 2x
  • C y = 2x - 4
  • D y = 2x2 - 4

Question - 7

The order of the differential equation whose general solution is given by y = (c1 + c2) sine (x + c3) - c1ex + c5, is

  • A 5
  • B 4
  • C 2
  • D 3

Question - 8

If y1 and y2 are solutions of a differential equation then which of the following is also the solution of the differential equation

  • A c1y1 + c2y2 
  • B \(\frac { { y }_{ 1 } }{ { y }_{ 2 } } \)
  • C y1y2 
  • D \({ y }_{ 1 }^{ 2 }+{ y }_{ 2 }^{ 2 }\)

Question - 9

The differential equation representing the family of curves given by the equation y = Aex + Be-x + C, is

  • A \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } =y\)
  • B \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } =\frac { dy }{ dx } \)
  • C \(\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } =\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } \)
  • D \({ \left( \frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } \right) }^{ 2 }+y=0\)

Question - 10

The displacement x of a particle moving in a straight line at time t is given by the relation \(x=A\sin { \left( \mu t+k \right) } \) The differential equation representing this phenomenon is

  • A \(\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } =-kx\)
  • B \(\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } =kx\)
  • C \(\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } ={ u }^{ 2 }x\)
  • D \(\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } -{ u }^{ 2 }x\)
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