Let |x|=|y| e ^ x y- , , N be the solution of the differential equation x ~d y-y ~d x+x y(x ~d y+y ~d x)=0 , y(1)=2 . Then + is equal to ________

Step-by-step solution

aligned & a|x|=|y| e^ y x- , a, b N & x d y-y d x+x y(x d y+y d x)=0 & d y y - d x x +(x d y+y d x)=0 & n|y|- n|x|+x y=c & y(1)=2 & n|2|-0+2=c & c=2+ n 2 & n|y|- n|x|+x y=2+ n 2 & n|x|= n | y 2 |-2+x y & |x|= | y 2 | e^ x y-2 & 2|x|=|y| e^ x y-2 & =2 =2 + =4 aligned