The integrating factor of x dydx + 1 +&n

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

111.

The integrating factor of the differential equation ylogydx = logy - xdy is

  • 1logy

  • loglogy

  • 1 + logy

  • logy


112.

The solution of the differential equation dydx = 1x + y2 is

  • y = - x2 - 2x - 2 + cex

  • y = x2 + 2x + 2 - cex

  • x = - y2 - 2y + 2 - cey

  • x = - y2 - 2y - 2 + cey


113.

The solution of the equation 3 + 22x2 - 8 + 3 + 228 - x2 = 6 are

  • 3 ± 22

  • ± 1

  • ± 33, ± 22

  • ± 3, ± 7


114.

The family of curves y = easin(x), where a is anarbitrary constant, is represented by thedifferential equation 

  • logy = tanxdydx

  • ylogy = tanxdydx

  • ylogy = sinxdydx

  • logy = cosxdydx


Advertisement
Advertisement

115.

The integrating factor of x dydx + 1 + x y = x is

  • x

  • 2x

  • exlog(x)

  • xex


D.

xex

Given differential equation is

xdydx + 1 + xy = x dydx + 1 + xxy = 1Which is linear differential equationHence, IF = e1 + xxdx = e1x + 1dx                = elogx + x                = elogx . ex                = xex


Advertisement
116.

The solution of the differential equation dydx + 1 = ex + y is

  • x + ex + y = c

  • x - ex + y = c

  • x + e- (x + y) = c

  • x - e- (x + y) = c


117.

The degree and order of the differential equation y = px + a2p2 + b23, where p = dydx, are respectively.

  • 3, 1

  • 1, 3

  • 1, 1

  • 3, 3


118.

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

  • order 1, degree 2

  • order 1, degree 3

  • order 2, degree 3

  • order 2, degree 2


Advertisement
119.

An integrating factor of the differential equation 1 + x2dydx + xy = x is

  • x1 + x2

  • 12log1 + x2

  • 1 + x2

  • x


120.

The solution of the differential equation xdydx + y = 1x2 at (1, 2) is

  • x2y + 1 = 3x

  • x2y + 1 = 0

  • xy + 1 = 3x

  • x2(y + 1) = 3x


Advertisement