UPSC NDA I 2021 Mathematics Solved Paper

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 .