UPSC NDA Math Model Paper 7

Given,

d2y

dx2

+sin‌x=0

d2y

dx2

=−sin‌x
Integrating, we get
⇒

dy

dx

=cos‌x+c1
Again integrating, we get
⇒y=sin‌x+c1x+c2
A solution of a differential equation is a relation between the variables (independent and dependent), which is free of derivatives of any order, and which satisfies the differential equation identically.
The solution of the differential equation

d2y

dx2

+sin‌x=0 is y=sin‌x+c1x+c2