Question

16. a.) Show that Y. and Y2 = In x are both solutions of the non-linear differential equation y' + (y') = 0 by substituting. b.) Is Y + Y also a solution, yes or no? Demonstrate by substituting,

Answer 1

a) Given :- y"+(40)*= 0 - 0 9,-1, Y = 6(x) 2. Consider, y,=1 c. Y;-0 i y'=0 Substitueting in eqn 0, we get 0+ (0)°= 0+0 RoHS - y, al is solution of equo Now yoz lnce) Y = 1 and .. . Y+(:)!= zz+Gá)? = "7+ =0 2 y 2 + (y! ²0 Hence Y,= ln (x) is solution of eq? 0 C2 2

b) Now consider | 9+yo – + Don(x) ... (9,42)'= 아 스 (t 굹 1. (4)-[H] + ) | 1 - Yo Yo is also solution of eg? ⓒ Cyt(9) - C + C, In(x) . Cute) + : ts) - - 2. (C4+ Cus) PC + say] - - + ( 20 , + . . XC 0 1 Hence YGtlty is not soluhon.