Answer in Differential Equations

Given

“x^2p^2+xyp+2y^2=0”

Let us denote “xp=q” ,thus we get “q^2+yq+2y^2=0” , now solving q ,we get,

“q=frac{-ypmsqrt{y^2-4cdot 1cdot 2y^2}}{2}\nimplies q=frac{-ypm ysqrt{7}i}{2}\nimplies xp=xfrac{dy}{dx}=y(-1pmsqrt{7}i)\nimplies frac{dy}{y}=(-1pmsqrt{7}i)frac{dx}{x}\nimplies intfrac{dy}{y}=(-1pmsqrt{7}i)intfrac{dx}{x}\nimplies ln y=-1pmsqrt{7}iln x+ln c\nimplies y=cx^{-1pmsqrt{7}i}”

Where c is constant and “i=sqrt{-1}”

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