Question Number 68308 by mr W last updated on 08/Sep/19 $${solve}\:{y}'''={y}''{y}' \\ $$ Answered by mind is power last updated on 08/Sep/19 $$\frac{{y}^{'''} }{{y}'^{'} }={y}'…
Question Number 133776 by bramlexs22 last updated on 24/Feb/21 $$\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:=\:\mathrm{sin}\:\mathrm{3x}\:+\:\mathrm{e}^{\mathrm{x}} \:+\:\mathrm{x}^{\mathrm{2}} \:,\:\mathrm{when}\:\mathrm{y}'\left(\mathrm{0}\right)=\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{y}\left(\mathrm{0}\right)=\:\mathrm{0}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{solution} \\ $$ Answered by bobhans last updated on 24/Feb/21…
Question Number 2602 by Yozzis last updated on 23/Nov/15 $${Solve}\:{the}\:{following}\:{d}.{e}\:{for}\:{v}\:{in}\:{terms}\:{of}\:{s} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{c}−{kv}={v}\frac{{dv}}{{ds}}. \\ $$$$ \\ $$ Answered by prakash jain last updated on 24/Nov/15 $$\frac{{vdv}}{{c}−{kv}}={ds}…
Question Number 68133 by mr W last updated on 05/Sep/19 $${solve}\:{y}''={y}'{y} \\ $$ Answered by mind is power last updated on 05/Sep/19 $$\Rightarrow{y}^{'} =\frac{{y}^{\mathrm{2}} }{\mathrm{2}}+{s}…
Question Number 68113 by Joel122 last updated on 05/Sep/19 $$\mathrm{Solve} \\ $$$${y}.{y}''\:=\:\mathrm{3}\left({y}'\right)^{\mathrm{2}} \\ $$ Answered by Smail last updated on 05/Sep/19 $$\Leftrightarrow\frac{{y}''}{{y}'}=\mathrm{3}\frac{{y}'}{{y}} \\ $$$${ln}\mid{y}'\mid=\mathrm{3}{ln}\mid{y}\mid+{c} \\…
Question Number 133631 by liberty last updated on 23/Feb/21 $$\mathrm{y}'\:=\:\frac{\mathrm{bx}+\mathrm{ay}}{\mathrm{ax}+\mathrm{by}} \\ $$ Answered by TheSupreme last updated on 23/Feb/21 $${caso}\:\mathrm{1}:\:{b}=\mathrm{0}\: \\ $$$${y}'=\frac{{ay}}{{ax}}=\frac{{y}}{{x}} \\ $$$${ln}\left({y}\right)={ln}\left({x}\right)+{c} \\…
Question Number 133570 by Ahmed1hamouda last updated on 23/Feb/21 Commented by Ahmed1hamouda last updated on 23/Feb/21 Solve the differential equations Commented by EDWIN88 last updated on 23/Feb/21 $$…
Question Number 67991 by ramirez105 last updated on 03/Sep/19 Commented by mathmax by abdo last updated on 03/Sep/19 $${xy}\:{dx}+\mathrm{2}\left({x}^{\mathrm{2}} \:+\mathrm{2}{y}^{\mathrm{2}} \right){dy}\:=\mathrm{0}\:\Rightarrow\mathrm{2}\left({x}^{\mathrm{2}} \:+\mathrm{2}{y}^{\mathrm{2}} \right){dy}\:=−{xydx}\:\Rightarrow \\ $$$$\mathrm{2}\frac{{dy}}{{y}}\:=\frac{−{xdx}}{{x}^{\mathrm{2}}…
Question Number 133508 by Ahmed1hamouda last updated on 22/Feb/21 Commented by Ahmed1hamouda last updated on 22/Feb/21 $$\boldsymbol{\mathrm{S}}\mathrm{olve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equations} \\ $$ Answered by Olaf last updated on…
Question Number 67939 by ramirez105 last updated on 02/Sep/19 Commented by mr W last updated on 02/Sep/19 $${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}…