Solve the following differential equation: `(dy)/(dx)=sec(x+y)`

Explanation

`text { Put } x+y=t`

`frac{d y}{d x}=\frac{d t}{d x}-1`

`frac{d t}{d x}-1={sect}`

`frac{d t}{d x}={sect}+1`

`int \frac{d t}{{sect}+1}=\int d x`

`int \frac{\cos t d t}{1+\cos t} d t=x`

`int \frac{1+\cos t d t-1}{1+\cos t} d t=x`

`int(d t-\frac{1}{1+\cos t}) d t=x`

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