UPSC NDA Math Model Paper 3

Given differential equation is
log(

dy

dx

)=2x+3y
⇒

dy

dx

=e(2x+3y)
⇒

dy

dx

=e2xe3y
⇒

dy

e3y

=e2xdx
Integrating both sides, we get
⇒∫e−3ydy=∫e2xdx
⇒

e−3y

−3

=

e2x

2

+c
⇒2e−3y=−3e2x−6c .......(1)
By using y = 0 when x = 0, we get
⇒ 2 = -3 – 6c
∴ c = -5/6
Put the value of c in equation 1st
⇒2e−3y=−3e2x−6(−5∕6)
⇒2e−3y=−3e2x+5
⇒2e−3y+3e2x=5