Solve the differential equation `(1+x^(2))(dy)/(dx)=x`.

Explanation

`(1+x^(2))(dy)/(dx)=x`
Integrate both sides with respect to `x`
`(dy)/(dx)=(x)/(1+x^(2))`
Integrate both sides with respect to `x`
`(dy)/(dx)*-dx=int(x)/(1+x^(2))dx+c` Let `1+x^(2)=t`
`implies int dy=int(x)/(1+x^(2))+cimplies2x=(dt)/(dx)`
`implies y=int(dt)/(dx)+cimpliesxdx=(dt)/(2)`
`implies y=(1)/(2)logt+c`
`impliesy=(1)/(2)log(1+x^(2))+c`.