Solve `(dy)/(dx)=(x+y)^2`

Explanation

`(dy)/(dx) = (x+y)^(2)`………………(1)
Here direct variables separation is not possible.
So, we choose substitution method.
Let x+y=v.
`therefore 1+(dy)/(dx)=(dv)/(dx)`
So,equation (1), reduces to
`(dv)/(dx)=v^(2)+1`
or `int(dv)/(v^(2)+1)=intdx`
`therefore tan^(-1)v=x+c`
`rArr x+y=tan(x+c)`, which is required solution.