Question

Find the particular solution of the differential equation `dy/dx = y cot 2x`, given that `y(pi/4) = 2.`

Answer 1

`dy/dx = ycot2x`

Given y = 2, x = `pi/4`

⇒ `dy/y = cot2x dx`

⇒ `intdy/y = intcot2x dx`

⇒ `log y = 1/2 log |sin 2x| + log C`

⇒ `log 4/sqrt (sin 2x) = log C`

⇒ `y/sqrt(sin^2x) = C`   ...(i)

Put `x=pi/4, y=2` in eq (i)

⇒ C = 2

Hence `[y= 2sqrt(sin2x)]`