Solve the given initial-value problem. the de is of the form dy dx = f(ax + by + c), which is given in (5) of section 2.5. dy dx = cos(x + y), y(0) = π 2

Let , so that :

Now the ODE is separable, and we have

Integrating both sides gives

For the integral on the left, rewrite the integrand as

Then

and so

Given that , we find

so that the particular solution to this IVP is