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 CExplanation: We have D1:y=4dydx+3xdxdy⇒ydydx=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)2⇒1+2dydx=0 ∴ Order=1, Degree=1 ∴ Required ratio = 1+2+12+3+1=46=23