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1)

Consider the following  differential equations.

D1:y=4dydx+3xdxdy;D2:d2ydx2=(3+(dydx)2)4/3

D3:[1+(dydx)]2=(dydx)2

 The ratio of the sum of the orders of D1,D2 and D3  to the sum of their degrees is 


A) 1:2

B) 1:1

C) 2:3

D) 3:2

Answer:

Option C

Explanation:

 We have

D1:y=4dydx+3xdxdyydydx=4(dydx)2+3x 

   Order=1, Degree=2

D2:d2ydx2=(3+(dydx)2)4/3

   =  (d2ydx2)3=(3+(dydx)2)4

     Order=2, Degree=3

D3:[1+(dyx)]2=(dydx)2

    1+(dydx)2+2dydx=(dydx)21+2dydx=0 

     Order=1, Degree=1

    Required ratio = 1+2+12+3+1=46=23