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Question Number 133403 by Engr_Jidda last updated on 21/Feb/21
$${verify}\:{that}\:\varrho^{{x}} \:{and}\:{x}\:{are}\:{the}\:{solution} \\ $$ $${of}\:{the}\:{homogeneous}\:{equation}\:{corresponding} \\ $$ $${to}\:\left(\mathrm{1}−{x}\right){y}^{\mathrm{2}} +{xy}^{\mathrm{1}} −{y}=\mathrm{2}\left({x}−\mathrm{1}\right)^{\mathrm{2}} \varrho^{{x}\:} ,\:\mathrm{0}<{x}<\mathrm{1} \\ $$ $${and}\:{find}\:{the}\:{general}\:{solution}. \\ $$