Q58 of 462 Page 23

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 =


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