UPSC NDA Math Model Paper 9

Given that,
⇒(

d2y

dx2

+

dy

dx

)

1

6

=(

dy

dx

+x)

1

3

As we can see above equation is not in proper form of polynomial so first we make it in polynomial form,
Multiply by 6 to the both side of power of terms,
⇒(

d2y

dx2

+

dy

dx

)

1

6

×6=(

dy

dx

+x)

1

3

×6
⇒(

d2y

dx2

+

dy

dx

)1=(

dy

dx

+x)2
⇒

d2y

dx2

+

dy

dx

=(

dy

dx

)2+2

dy

dx

x+x2 [∵(a+b)2=a2+2ab+b2]
⇒

d2y

dx2

+

dy

dx

−(

dy

dx

)2−2x.

dy

dx

−x2=0
Now we can say about the degree and order,
Degree = 1
Order = 2