The solution of the differential equationxy2dy - x3&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

351.

The solution of 1 + x2dydx + 2xy - 4x2 = 0 is :

  • 3x1 + y2 = 4y3 + c

  • 3y(1 + x2) = 4x3 + c

  • 3x(1 + y2) = 4y3 + c

  • 3y(1 + y2) = 4x3 + c


352.

The solution of dxdy + xy = x2 is :

  • 1y = cx - xlogx

  • 1x = cy - ylogy

  • 1x = cx + xlogy

  • 1y = cx - ylogx


353.

The differential equation obtained by eliminating the arbitrary constants a and b from xy = aex + be- x is

  • xd2ydx2 +2dydx - xy = 0

  • xd2ydx2 +2ydydx - xy = 0

  • xd2ydx2 +2dydx + xy = 0

  • d2ydx2 +dydx - xy = 0


354.

The solution of x + y +1dydx = 1 is

  • y = (x + 2) + cex

  • y = - (x + 2) + cex

  • x = - (y + 2) + cey

  • x = (y + 2)2 + cey


Advertisement
355.

The solution of dydx = y2xy - x2 is

  • eyx = kx

  • eyx = ky

  • exy = kx

  • e - yx = ky


356.

The solution of dydx +1 = ex +y is

  • e - x + y +x + c = 0

  • e - x + y -x + c = 0

  • e x + y +x + c = 0

  • e x + y -x + c = 0


357.

The solution of the differential equation

dydx = xy + yxy + x is

  • x + y = logcyx

  • x + y = logcxy

  • x - y - logcxy

  •  y - x = logcxy


358.

The solution of the differential equation

dydx = x - 2y + 12x - 4y is

  • (x - 2y)2 + 2x = c

  • (x - 2y)2 + x = c

  • (x - 2y)2 + 2x2 = c

  • (x - 2y) + x2 = c


Advertisement
359.

The solution of the differential equation dydx - ytanx = exsecx is

  • y = excosx + c

  • ycosx = ex + c

  • y = exsinx + c 

  • ysinx = ex + c


Advertisement

360.

The solution of the differential equation

xy2dy - x3 + y3dx = 0 is

  • y3 = 3x3 + c

  • y3 = 3x3 logcx

  • y3 = 3x3 + logcx

  • y3 +3x3 = logcx


B.

y3 = 3x3 logcx

Given differential equation can be rewritten asdydx = x3 + y3xy2It is a homogeneous differential equation.Put y = vx  dydx = v + xdvdx xdvdx +v = x3 + v3x3xy2It is a homogeneous differential equation.Put y = vx  dydx = v + xdvdx xdvdx +v = x3 + v3x3 x3v2  xdvdx +v = 1 + v3v2 xdvdx = 1v2 v2dv = dxxOn integrating both sides, we getv33 = logx + logc13yx3 =logx + logc y3 = 3x3logcx


Advertisement
Advertisement