The solution of the differential equation `dy/dx=sin(x+y)+cos(x+y)` is:

Explanation

`dy/dx=sin(x+y)+cos(x+y)`

Let x+y=t

`dt/dx=1+sint+cost`

`intdt/(1+sint+cost)=intdx`

`intdt/(1+(2tant/2)/(1+tan^2t/2)+(1-tan^2t/2)/(1+tan^2t/2))=x`

`int(sec^2t/2dt)/(2(tant/2+1))=x`

`1+tant/2=h`

`1/2sec^2t/2dt=dh`
`int(dh)/h=x`

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