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)
u=x+yu=x+yu=x+y
y′=u′−1y'=u'-1y′=u′−1
u′−cosu−1=0u'-cosu-1=0u′−cosu−1=0
u′cosu+1=1\frac{u'}{cosu+1}=1cosu+1u′=1
ducosu+1=dx\frac{du}{cosu+1}=dxcosu+1du=dx
∫ducosu+1=∫dx\int\frac{du}{cosu+1}=\int dx∫cosu+1du=∫dx
tan(u/2)=x+ctan(u/2)=x+ctan(u/2)=x+c
tan((x+y)/2)=x+ctan((x+y)/2)=x+ctan((x+y)/2)=x+c
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