Question

Solution of the differential equation 2y sinx.dy/dx  = 2 sin x cos x – y² cos x satisfying y(π/2) = 1  is

(a)   y² = sin x 

(b)   y = sin² x 

(c)   y² = cos x +1 

(d)   None of these

Answer 1

Correct option  (a) y² = sin x

Explanation:

(2ydy/dx) sinx + y²  cosx = sin 2x

d/dx(y² sinx) = sin 2x

Integrating both sides,

y² sin x = -1/2 soc2x + C

Now yπ/2 = 1

1.sinπ/2 = -1/2.(-1) + C

C = 1/2

y² sin x = 1/2(1 - cos 2x)

y² sin x = 1/2.2 sin²x

y² = sin x