If x2y - x3dydx = y4cosx, then 

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341.

Soution of dydx = xlogx2 + xsiny + ycosy is

  • ysiny = x2logx + C

  • ysiny = x2 + C

  • ysiny = x2 + logx

  • ysiny = xlogx + C


342.

The general solution of y2dx + x2 - xy + y2dy = 0 is :

  • tan-1yx = logy + C

  • 2tan-1xy + logx + C = 0

  • logy + x2 + y2 + logy + C = 0

  • sinh-1xy + logy + C = 0


343.

Integrating factor of (x + 2y3)dydx = y2 is

  • e1y

  • e- 1y

  • y

  • - 1y


344.

y = Aex + Be2x + Ce3x satisfies the differential equation

  • y''' - 6y'' + 11y' - 6y = 0

  • y''' + 6y'' + 11y' + 6y = 0

  • y''' + 6y'' - 11y' + 6y = 0

  • y''' - 6y'' - 11y' + 6y = 0


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345.

Observe the following statements

A. Integrating factor of dydx + y = x2 is ex

R. Integrating factor of dydx + Pxy = Qx is ePxdx

  • A is true, R is false

  • A is false, R is true

  • A is true, R is true, R  A

  • Both are false


346.

If dx + dy = (x + y)dx - dy, then logx + y = ?

  • x + y + c

  • x + 2y + c

  • x - y + c

  • 2x + y + c


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347.

If x2y - x3dydx = y4cosx, then x3y- 3 is equal to

  • sin(x)

  • 2sin(x) + c

  • - 3sin(x) + c

  • 3cos(x) + c


C.

- 3sin(x) + c

Given that

x2y - x3dydx = y4cosx On dividing by y4, we getx2y3 - x3y4dydx = cosxx3y4dydx = x2y3 - cosx 1y4dydx - 1xy3 = - 1x3cos(x)Let     - 1y3 = t 1y4dydx = 13dtdx 13dtdx + tx = 1x3cos(x)  dtdx + 3tx = 3x3cos(x)This is differential equation in t, On compairing with dtdx + Pt = Q, we getP = 3x, Q =  3x3cos(x) I.F. = epdx =  e3xdx  = elogx3 = x3 Complete solution is tx3 = 3x3x3cos(x)dx +c1 tx3 = 3sin(x) + c1 - 1y3x3 = 3sin(x) + c1 y- 3x3 = - 3sinx +c


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348.

Observe the following statements

I. If dy +2xydx = 2e- x2dx, then yex2 = 2x + c,II. If ye- x2 - 2x = c, thendx = 2e- x2 - 2xydywhich of the following is correct statement

  • Both I and II are true

  • Neither I nor II is true

  • I is false, But II is true

  • I is true, But II is false


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349.

If dydx = y +xtanyxx, then sinyx is equal to

  • cx2

  • cx

  • cx3

  • cx4


350.

The solution of x2 + y2dx = 2xydy is :

  • cx2 - y2 = x

  • cx2 + y2 = x

  • cx2 - y2 = y

  • cx2 + y2 = y


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