The solution of cosydydx = ex + siny&nbs

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

101.

If the integrating factor of the differential equation dydx + Pxy = Qx is x, then P(x) is

  • x

  • x2/2

  • 1/x

  • 1/x2


102.

If c1, c2, c3, c4, c5 and c6  are constants, then the order of the differential equation whose general solution is given by y = c1 cos(x + c2) + c3 sin(x + c4) + c5ex + c6, is

  • 6

  • 5

  • 4

  • 3


103.

y = 2e2x - e- x is solution of the differential equation

  • y2 + y1 + 2y = 0

  • y2 - y1 + 2y = 0

  • y2 + y1 = 0

  • y2 - y1 - 2y = 0


104.

If xdy = y(dx + y dy), y(1) = 1 and y(x) > 0, then y(- 3) is equal to

  • 3

  • 2

  • 1

  • 0


Advertisement
105.

The differential equation representing the family of curves y = 2c (x + c3), where c is a positive parameter, is of

  • order 1, degree 1

  • order 1, degree 2

  • order 1, degree 3

  • order 1, degree 4


106.

The differential equation representing the family of curves y = xecx (c is a constant) is

  • dydx = yx1 - logyx

  • dydx = yxlogyx + 1

  • dydx = yx1 + logyx

  • dydx +1 = yxlogyx


107.

The solution of dydx = 1 + y + y2 + x + xy + xy2 is

  • tan-12y + 13 = x + xy + xy2

  • 4tan-12y + 13 = 322x + x2

  • 3tan-13y + 13 = 41 +x +x2 + c

  • tan-12y + 13 = 32x + x2 + c


108.

The integrating factor of the differential equation

dydx + y1 - xx = 1 - x is

  • 1 - x1 + x

  • 1 + x1 - x

  • 1 - x1 +x

  • x1 - x


Advertisement
Advertisement

109.

The solution of cosydydx = ex + siny + x2esiny is

  •  ex - e- siny+ x33 = c

  •  e- x - e- siny+ x33 = c

  •  ex + e- siny+ x33 = c

  •  ex - esiny+ x33 = c


C.

 ex + e- siny+ x33 = c

Given, cosydydx = ex + siny + x2esiny cosydydx = esinyex + x2dx cosyesinydy = ex + x2dxPut siny = t in LHS  cosydy = dt dtet = ex + x2dx - e- t = ex + x33 - c ex + e- siny + x33 = c


Advertisement
110.

The order and degree of the differential equation

1 + dydx234 = d2ydx213

  • (2, 4)

  • (2, 3)

  • (6, 4)

  • (6, 9)


Advertisement