Solve `x^2((dy)/(dx))+y=1`

Explanation

The given differential equation can be written as
`(dy)/(dx) +1/x^(2)y=1/x^(2)`, which is linear
Here, `P=1//x^(2)` and Q`=1/x^(2)`
I.F. `e^(int(1//x^(2))dx) = e^(-1//x)`
Therefore, the solution is
`ye^(-1//x) = inte^(-1//x)(1//x^(2))dx+c=e^(-1//x)+c`
or `y=1+ce^(1//x)`