Show that the substitution $$\(y^{2}=w \sin 2 x\)$$, where $$\(w\)$$ is a function of $$\(x\)$$, transforms the differential equation $$\[ y \frac{\mathrm{d} y}{\mathrm{~d} x}+y^{2} \tan x=\sin x \quad 0< x< \frac{\pi}{2} \]$$ (I) into the differential equation $$\[ \frac{\mathrm{d} w}{\mathrm{~d} x}+2 w \operatorname{cosec} 2 x=\sec x \quad 0< x< \frac{\pi}{2} \]$$ (II) (4)

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