Solve the following differential equation: `(1+y+x^2)dx+(x+x^3)dy=0`

Explanation

We have `(1+y+x^(2)y)dx+(x+x^(3))dy=0`
`rArr 1+y(1+x^(2))+x(1+x^(2))(dy)/(dx)=0`
`rArr (dy)/(dx) +y/x=-1/(x(1+x^(2))`, which is linear differential equation.
I.F. `=e^(int1/xdx) = e^(log_(e)x)=x`
`therefore` Solution is `y xx x=-int1/(1+x^(2))dx`
`therefore y xx x=-tan^(-1)x+c`