BITSAT 2019 Paper

(b) Given differential equation is :
x cosx dy / dx + y (x sinx + cosx) = 1
Dividing both the sides by x cos x,
⇒

dy

dx

+

xy‌sinx

x‌cosx

+

y‌cosx

x‌cosx

=

1

x‌cosx

⇒

dy

dx

+ y tan x +

y

x

=

secx

x

⇒

dy

dx

+ (tan‌x+

y

x

)y =

sec‌x

x

which is of the form

dy

dx

+ P y = Q
Here,P = tan x +

1

x

and Q =

sec‌x

x

Integrating factor = e‌∫Pdx = e‌∫tan‌x+

1

x

dx
= e‌(log‌sec‌x+log‌x) = e‌log(sec‌x.x) = x sec x