The solution of the equation dydx = 1x + 

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

Advertisement

321.

The solution of the equation dydx = 1x + y + 1 is

  • x + y = Cey - 2

  • x + y = Clog(y) - 4

  • log(x+ y + 2) = Cy

  • log(x + y + 2) = C + y


D.

log(x + y + 2) = C + y

Given differential equaton is              dydx = 1x + y + 1or          dxdy = x + y + 1 dxdy - x = y + 1Eq (i) is of the type dxdy + Px = Q,where P and Q are  functions of y or constant termsHere, P = - 1and   Q = y + 1    IF = ePdy = e- 1dy = e- y

Now, general solution is given by        x . IF = IF . Qdy + C1 x . e-y = e-yIy + 1IIdy +C1    xe-y = y + 1e-y- 1 + 1 . e-ydy + C1    xe-y = e-yy + 1 - e-y + C1         x = - y + 1 - 1 + C1ey                   on dividing by e-y x + y + 2 = C1eyOn taking log both sides, we get

      logx + y + 2 = logC1ey logx + y + 2 = logC1 + logey         logmn = logm + logn logx + y + 2 = C + y         put C  = logC1

which is the required solution.


Advertisement
322.

The solution of differential equation (ylog(x) - 1)ydx = xdy is

  • ylogex + Cx = 1

  • logxe + Cxx = y

  • logCx2 + ex2y = x

  • None of these


323.

The solution of the differential equation a + xdydx + xy = 0 is

  • y = Ce232a  - xx + a

  • y = Ce23a  - xx + a

  • y = Ce232a  + xx + a

  • y = Ce- 232a  - xx + a


324.

The general solution of the differential equation dydx = ytanx - y2secx is

  • tanx = C + secxy

  • secy = C + tanyx

  • secx = C + tanxy

  • tany = C + secxx


Advertisement
325.

The degree of the differential equation satisfying 1 - x2 + 1 - y2 = ax - y is

  • 1

  • 2

  • 3

  • None of the above


326.

The solution of the differential equation y - xdydx = ay2 + dydx is

  • y = C(x + a)(1 - ay)

  • y = C(x + a)(a + ay)

  • y = C(x - a)(1 - ay)

  • None of the above


327.

The solution of differential equation (2y - 1)dx - (2x + 3)dy = 0 will be

  • 2x - 12y + 3 = C

  • 2y + 12x - 3 = C

  • 2x + 32y - 1 = C

  • 2x - 12y - 1 = C


328.

The solution of the differential equation dydx = xlogx2 + xsiny + ycosy will be

  • ysin(y) = x2log(x) + C

  • ysin(y) = x2 + C

  • ysin(y) = x2 + lo(x) + C

  • ysin(y) = xlog(x) + C


Advertisement
329.

The order and degree of the differential equation y'4 = 1 - y''' are respectively.

  • 3, 4

  • 1, 2

  • 3, 2

  • 3, 1


330.

The differential equation of the family of circles having centre on Y-axis and radius 4 is

  • x2 - 4dydx2 + x2 = 0

  • x2 - 9dydx2 + x2 = 0

  • x2 - 9dydx + x2 = 0

  • x2 - 16dydx2 + x2 = 0


Advertisement