Which of the following transformations reduce the differential equation `(dz)/(dx)+z/x log z=z/x^2 (log z)^2` into the form `(dv)/(dx)+P(x)v=Q(x)`

Explanation

`frac{d z}{d x}+frac{z}{x} log z=frac{z}{x^{2}}(log z)^{2}`



by dividing each side with `z(log z)^{2}` we get ,

`frac{d z}{z(log z)^{2} d x}+frac{z}{z(log z)^{2} x} log z=frac{z}{z(log z)^{2} x^{2}}(log z)^{2} `


`frac{d z}{z(log z)^{2} d x}+frac{1}{(log z) x}=frac{1}{x^{2}} `


` v=frac{1}{log z} `


` frac{d v}{d x}=frac{-1}{z(log z)^{2}} frac{d z}{d x} `


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