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Question - 1

The integrating factor of  \(\frac { dy }{ dx } +2\frac { y }{ x } -{ e }^{ 4x }\) is

  • A \(\log { x } \)
  • B \({ x }^{ 2 }\)
  • C \({ e }^{ x }\)
  • D x

Question - 2

If cos x is an integrating factor of the differential equation \(\frac { dy }{ dx } +Py=Q\) then P=

  • A – cot x
  • B cot x
  • C tan x
  • D – tan x

Question - 3

The integrating factor of dx + xdy = \({ e }^{ -\lambda }{ \quad sec }^{ 2 }y\quad dy\) is

  • A \({ e }^{ x }\)
  • B \({ e }^{ -x }\)
  • C \({ e }^{ y }\)
  • D \({ e }^{ -y }\)

Question - 4

Integrating factor of \(\frac { dy }{ dx } +\frac { 1 }{ x\log { x } } .y=\frac { 2 }{ { x }^{ 2 } } \) is

  • A \({ e }^{ x }\)
  • B \(\log { \quad x } \)
  • C \(\frac { 1 }{ x }\)
  • D \({ e }^{ -x }\)

Question - 5

Solution of \(\frac { dy }{ dx } +mx = 0\) when m < 0 is

  • A x = cemy
  • B x = ce-my
  • C x = my + c
  • D x = c

Question - 6

y = cx – c² is the general solution of the differential equation

  • A (y’)² - xy’ +y =0
  • B y’’ = 0
  • C y’=c
  • D (y’)² + xy’ + y = 0

Question - 7

The differential equation \({ \left( \frac { dy }{ dx } \right) }^{ 2 }+\quad { 5y }^{ { 1 }/{ 3 } }=x\) is

  • A of order 2 and degree 1
  • B of order 1 and degree 2
  • C of order 1 and degree 6
  • D of order 1 and degree 3

Question - 8

The differential equation of all non-vertical lines in a plane is

  • A \(\frac { dy }{ dx } =\quad 0\)
  • B \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } =\quad 0\)
  • C \(\frac { dy }{ dx } =\quad m\)
  • D \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } =\quad m\)

Question - 9

The differential equation of all circles with centre at the origin is

  • A xdy+ydx=0
  • B xdy-ydx=0
  • C xdx +ydy=0
  • D xdx -ydy=0

Question - 10

The integrating factor of the differential equation \(\frac { dy }{ dx } +Py=\quad Q\) is

  • A \(\int { Pdx } \)
  • B \(\int { Qdx } \)
  • C \({ e }^{ \int { Qdx } }\)
  • D \({ e }^{ \int { Pdx } }\)
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