The solution of the differential equation, d y ~d x =(x-y)² , when y(1)=1, is:

Step-by-step solution

The given differential equation d y d x =(x-y)² Let x-y=t 1- d y d x = d t d x d y d x =1- d t d x Now, from equation (1) (1- d t d x )=(t)² 1-t²= d t d x d x= d t 1-t² -x= 1 2 1 | t-1 t+1 |+c -x= 1 2 | x-y-1 x-y+1 |+c The given condition y(1)=1-1= 1 2 | 1-1-1 1-1+1 |+c c=-1 Hence, 2(x-1)=- | 1-x+y 1-y+x |