Question Number 129445 by Engr_Jidda last updated on 15/Jan/21
$${Solve}\:{the}\:{ODE}'{s}\:{using}\:{lipschitz}\:{condition} \\ $$$${with}\:{constant}\:{k}. \\ $$$$\left.\mathrm{1}\right)\:{f}\left({x},{y}\right)={x}^{\mathrm{2}} \varrho^{{x}+{y}} \\ $$$$\left.\mathrm{2}\right)\:{f}\left({x},{y}\right)={x}\mid{y}\mid \\ $$