In Problems $1-6,$ use $(1)$ to find the general solution of the given differential equation on $(0,).$

$x^2{y}^{\text{'}\text{'}}+x{y}^{\text{'}}+(x^2-\frac{1}{3})y=0$

$x^2{y}^{\text{'}\text{'}}+x{y}^{\text{'}}+(x^2-1)y=0$

$4x^2{y}^{\text{'}\text{'}}+4x{y}^{\text{'}}+(4x^2-25)y=0$

$16x^2{y}^{\text{'}\text{'}}+16x{y}^{\text{'}}+(16x^2-1)y=0$

$x{y}^{\text{'}\text{'}}+y^{\text{'}}+xy=0$

$\frac{dw}{w}+2\frac{y_1^{\text{'}}}{y_1}dx+Pdx=0$

please solve the question $4$ step by step and don't skip any process