Solve the differential equation: `(1+y^2) dx/dy + x = e^(tan^(-1)y)`

Explanation

Differential equation can be rewritten as
`(1+y^(2))(dx)/(dy) +x = e^(tan^(-1))y`
or `(dx)/(dy) + 1/(1+y^(2)).x=(e^(tan^(-1))y)/(1+y^(2))`
Here, I.F. `=e^(int1/(1+y^(2)dy)) = e^(tan^(-1)y)`
Solution is `xe^(tan^(-1)y)= inte^(tan^(-1)y)/(1+y^(2))e^(tan^(-1)y)dy`
`rArr xe^(tan^(-1)y)= (e^(2tan^(-1)y))/(2)+C`