Answer to Question #263031 in Differential Equations for Neilmar

Question

Solve the given differential equation by using an appropriate substitution. The DE is of the form dy dx = f(Ax + By + C)

dy/dx = cos(x + y)

Answer 1

$u=x+y$

$y'=u'-1$

$u'-cosu-1=0$

$\frac{u'}{cosu+1}=1$

$\frac{du}{cosu+1}=dx$

$\int\frac{du}{cosu+1}=\int dx$

$tan(u/2)=x+c$

$tan((x+y)/2)=x+c$