Concept: Order of a differential equation is the highest order of derivative that occurs in the differential equation. Degree of a differential equation is the highest power of the highest order derivative that occurs in the equation, after all the derivativesare converted into rational and radical free form. Calculation: y2+2cy−cx+c2=0 ⇒(y+c)2=cx ⇒2(y+c)y′=c ⇒c=
2yy′
1−2y′
Substituting this in the given equation, we get: (y+
2yy′
1−2y′
)2=
2yy′
1−2y′
x ⇒y2=2xyy′(1−2y′) ⇒y2−2xyy′+4xy(y′)2=0 The highest derivative in it is y ', therefore its order is 1 And, the highest power of this derivativein the equation is 2 , therefore its degree is 2 .