1.

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

Answer» `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`
`ln|h|+c=x`
`ln(1+tanh/2)+c=0`
`ln(1+tan((x+y)/2)+c=x`
`ln|tan((x+y)/2)+1|=x+c`.


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