If y(x) is a solution of and y(0) = 1, then find the value of

given:

To find: solution of the given differential equation

Re-writing the equation as

Integrating both sides

Let sin x=t

cos x dx=dt

formula:

Formula:

ln(1+y) = -ln(2+t)+log c

ln(1+y)+ln(2+sin x )=log c

(1+y)(2+sinx) = c

When x = 0 and y = 1

c = 4

If x = π/2 then,