The equation of a curve passing through the origin and satisfying the differential equation d y d x =(x-y)^2 is

Step-by-step solution

The given differential equation is d y d x =(x-y)^2 array ll Put & x-y=t & 1- d y d x = d t d x & d y d x =1- d t d x array array ll & 1- d t d x =t^2 & (1-t^2 )= d t d x array On integrating both sides, we get array rlrl 1 1-t^2 d t & = 1 d x & 1 2 ( 1+t 1-t ) & =x+c ( 1+t 1-t ) & =e^ 2 x+2 c 1+x-y 1-x+y & =A e^ 2 x array It passes through origin. A=1 Required curve is (1+x-y)=e^ 2 x (1-x+y)