If y(x) is a solution of the differential equation (2 + sin x)/(1 + y)dy/dx = -cos x

Question

If y(x) is a solution of the differential equation \(\left(\frac{2 + \text{sin x}}{\text{1 + y}}\right)\frac{\text{dy}}{\text{dx}}=-\text{cos x}\) and y(0) = 1, then find the value of y(π/2).

Answer 1

Consider the given equation

\(=\left(\frac{2 + \text{sin x}}{\text{1 + y}}\right)\frac{\text{dy}}{\text{dx}}=-\text{cos x}\)

Integrating both sides,

Substituting the value of C in eq (1), we get

Now, find the value of y(π/2)

Substituting the value of x = \(\frac{\pi}{2}\) in equation (2)