If y(x) is a solution of the differential equation and y(0) = 1, then find the value of y(π/2).
Consider the given equation
=
=
Integrating both sides,
=
= log(1 + y) ⟹-log(2 + sin x) + log C
= log(1 + y) + log(2 + sin x) = log C
= log(1 + y)(2 + sin x) = log C
= (1 + y)(2 + sin x) = c ….(1)
Given that y(0) = 1
= (1 + 1)(2 + sin 0) = c
= C = 4
Substituting the value of C in eq (1), we get
= (1 + y)(2 + sin x) = 4
= (1 + y) =
= y = ……(2)
Now, find the value of y(π/2)
Substituting the value of x = in equation (2)
= y =
= y =
= y =
= y =