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Q.

Match the differential equaitons in List-I to their integrating factors in List-II
List-I                                                      List-II
Differential equation                          Integrating factor

i)   (x3+1)dydx+x2 y=3x2           a)  x3

ii)  x2dydx+3xy=x6                        b)  (x3+1)2

iii) (x3+1)2dydx+  6x2(x3+1)y=x2                       c)  (x2+1)2

iv) (x2+1)dydx+4xy=ln x          d)  x2+1

                                                            e)  (x3+1)13

                                                            f)  (x3+1)12

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An Intiative by Sri Chaitanya

a

i ii iii iv

d a b c

b

i ii iii iv

e b c f

c

i ii iii iv

e a c d

d

i ii iii iv

e a b c

answer is B.

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Detailed Solution

Linear diff. eqn.

dydx+Py=QI.F=ePdx

(i)    x3+1 dydx+x2y=0dydx+x2x3+1y=0P=x2x3+1,  Q=0

            I.F=ex2x3+1dx =e13 log x3+1 =x3+113

(ii)   x2dydx+3xy=x6

        Divide with x2 both sides

      dydx+3xy=x4P=3x,  Q=x4I.F=e3x dx=e3log x=elog x3 =x3

(iii)   x3+12 dydx+6x2x3+1y=x2dydx+6x2x3+1=x3x3+1  P=6x2x3+1, Q=x2x3+1I.F=e6x2x3+1dx=e23x2x3+1dx =e2logx3+1=x3+12

(iv)   dydx+4xyx2+1=log xx3+1P=4xx2+1,  Q=log xx3+1I.F=e49x2+1dx =e2 2xx2+1dx =e2log x2+12 =x2+12

                        i    ii    iii    iv         e   a    b    c

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