If y=y(x) is the solution of the differential equation ( 2+ x y+1 ) d y d x + x=0 with y(0)=1 , then y ( 2 ) is equal to

Step-by-step solution

Given differential equation can be rewritten as d y 1+y + x 2+ x d x=0 Put 2+ x=t ( x) d x=d t d y 1+y + 1 t d t=0 On integrating, we get array rlrl (1+y)+ t = C (1+y) t =C (1+y)(2+ x) =C array when y(0)=1 array ll & (1+1)(2+0)=C C=4 & (1+y)(2+ x)=4 At x= 2 array array rlrl [1+y ( 2 ) ] [2+ 2 ]=4 1+y ( 2 ) = 4 3 y ( 2 ) = 1 3 array