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Question Number 132881 by Engr_Jidda last updated on 17/Feb/21
find the series solution of  the ordinary differential equation  y^2 +2xy^1 −3y=x^2 −1  y(0)=1 and y^1 (0)=2
$${find}\:{the}\:{series}\:{solution}\:{of} \\ $$$${the}\:{ordinary}\:{differential}\:{equation} \\ $$$${y}^{\mathrm{2}} +\mathrm{2}{xy}^{\mathrm{1}} −\mathrm{3}{y}={x}^{\mathrm{2}} −\mathrm{1} \\ $$$${y}\left(\mathrm{0}\right)=\mathrm{1}\:{and}\:{y}^{\mathrm{1}} \left(\mathrm{0}\right)=\mathrm{2} \\ $$

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