The differential equation, find a particular solution satisfying the given condition : dy/dx = y tan x, it being given that y = 1 when x = 0.

Question

The differential equation, find a particular solution satisfying the given condition : 

\(\frac{dy}{dx}\) = y tan x, it being given that y = 1 when x = 0.

Answer 1

Rearranging the terms we get:

\(\frac{dy}y\) = tan x dx

⇒ \(\int\frac{dy}y\) = \(\int{tanx}\,dx\) + c

⇒ log |y| = log |sec x| + log c 

⇒ log |y| - log |sec x| = log c 

⇒ log |y| + log |cos x| = log c 

⇒ y cos x = c y = 1 when x = 0 

∴1 × cos0 = c 

∴c = 1 

⇒ y cos x = 1 

⇒ y = 1/cos x 

⇒ y = sec x 

Ans: y = sec x