If y(x) is a solution of the differential equation and y(0) = 1, then find the value of y(π/2).

Question

Philoid · Accepted Answer

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 =