Category: Differential Equation

Question Number 67991 by ramirez105 last updated on 03/Sep/19 Commented by mathmax by abdo last updated on 03/Sep/19 $${xy}\:{dx}+\mathrm{2}\left({x}^{\mathrm{2}} \:+\mathrm{2}{y}^{\mathrm{2}} \right){dy}\:=\mathrm{0}\:\Rightarrow\mathrm{2}\left({x}^{\mathrm{2}} \:+\mathrm{2}{y}^{\mathrm{2}} \right){dy}\:=−{xydx}\:\Rightarrow \\ $$$$\mathrm{2}\frac{{dy}}{{y}}\:=\frac{−{xdx}}{{x}^{\mathrm{2}}…

Question Number 67939 by ramirez105 last updated on 02/Sep/19 Commented by mr W last updated on 02/Sep/19 $${sir},\:{you}\:{got}\:{y}^{\mathrm{2}} \left({y}+\mathrm{2}{x}\right)={C},\:{but}\:{this} \\ $$$${doesn}'{t}\:{satisfy}\:{the}\:{original}\:{equ}. \\ $$$${is}\: \\ $$$$\frac{{dy}}{{y}}\:=−\frac{{dx}}{\mathrm{2}{x}+\mathrm{3}{y}}\:\Rightarrow\int\:\frac{{dy}}{{y}}\:=−\int\frac{{dx}}{\mathrm{2}{x}+\mathrm{3}{y}}\:+{c}…

Question Number 67900 by ramirez105 last updated on 02/Sep/19 $${homogenous}\:{differential}\:{equation}. \\ $$$${please}\:{answer}. \\ $$$${y}\left({x}^{\mathrm{2}} +{xy}−\mathrm{2}{y}^{\mathrm{2}} \right){dx}+{x}\left(\mathrm{3}{y}^{\mathrm{2}} −{xy}−{x}^{\mathrm{2}} \right)\mathrm{2}{y}=\mathrm{0} \\ $$$$ \\ $$$${can}\:{someone}\:{answer}\:{this}?? \\ $$ Terms…

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

Question Number 133353 by Ahmed1hamouda last updated on 21/Feb/21 Commented by Ahmed1hamouda last updated on 21/Feb/21 $$\:\boldsymbol{{solve}}\:\boldsymbol{{the}}\:\boldsymbol{{differential}}\:\boldsymbol{{equation}}\mathrm{s} \\ $$ Answered by mathmax by abdo last…