Find the general solution of each of the following differential equations:
`(1)/(x)*(dy)/(dx)=tan^(-1)x`

Answer

`y=(1)/(2)(x^(2)+1)tan^(-1)x-(1)/(2)x+C`

Explanation

`intdy = int (underset(I)(tan^(-1))x)underset(II)(x) dx rArr y=(tan^(-1)x)(x^(2))/(2)-int (1)/((1+x^(2)))*(x^(2))/(2)dx +C`
`rArr y = (1)/(2)x^(2)(tan^(-1)x)-(1)/(2)int{((1+x^(2))-1)/((1+x^(2)))}dx +C.`
`rArr y =(1)/(2)x^(2)(tan^(-1)x)-(1)/(2)int{1-(1)/((1+x^(2)))}dx +C`.