Question Number 13976 by tawa tawa last updated on 25/May/17 $$\mathrm{Solve}: \\ $$$$\mathrm{x}^{\mathrm{2}} \left(\mathrm{y}\:+\:\mathrm{1}\right)\:+\:\mathrm{y}^{\mathrm{2}} \left(\mathrm{x}\:−\:\mathrm{1}\right)\mathrm{y}'\:=\:\mathrm{0} \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 25/May/17 $${y}^{'}…
Question Number 79469 by M±th+et£s last updated on 25/Jan/20 $${Q}.{solve} \\ $$$$−\frac{{d}^{\mathrm{2}} {y}}{{dt}^{\mathrm{2}} }−{coth}\left({t}\right)\frac{{dy}}{{dt}}+\left(\mathrm{20}+\frac{\mathrm{4}}{{sinh}^{\mathrm{2}} \left({t}\right)}\right){y}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 13649 by ajfour last updated on 22/May/17 $$\mathrm{2}{xyy}'+\left({x}−\mathrm{1}\right){y}^{\mathrm{2}} ={x}^{\mathrm{2}} {e}^{{x}} \\ $$ Answered by ajfour last updated on 22/May/17 $${let}\:{y}^{\mathrm{2}} ={tx}\:\:\:\:\:\Rightarrow\:\:\:\mathrm{2}{yy}'={t}+{x}\frac{{dt}}{{dx}} \\ $$$${substituting}…
Question Number 13626 by tawa tawa last updated on 21/May/17 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{cosech}^{−\mathrm{1}} \left(\mathrm{x}\right)\:=\:\mathrm{sinh}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{x}}\right) \\ $$ Answered by mrW1 last updated on 21/May/17 $${u}=\mathrm{cosech}^{−\mathrm{1}}…
Question Number 144608 by ArielVyny last updated on 26/Jun/21 $${find}\:{all}\:{aplication}\:{f}\:{in}\:\mathbb{R}\rightarrow\mathbb{R}\:\:{f}\in{C}^{\mathrm{2}} \\ $$$$\forall{x}\in\mathbb{R}.\:\:{f}''\left({x}\right)+{f}\left(−{x}\right)={x} \\ $$ Answered by Olaf_Thorendsen last updated on 27/Jun/21 $${f}''\left({x}\right)+{f}\left(−{x}\right)\:=\:{x}\:\:\:\left(\mathrm{1}\right) \\ $$$$\mathrm{Let}\:{u}\left({x}\right)\:=\:{f}\left({x}\right)+{x} \\…
Question Number 78878 by M±th+et£s last updated on 21/Jan/20 $${x}^{\mathrm{3}} \:{y}'''\:−\:\mathrm{3}{x}^{\mathrm{2}} {y}''+\mathrm{6}{xy}'\:−\mathrm{6}{y}={x}^{\mathrm{4}} \:{ln}\left({x}\right),{x}>\mathrm{0} \\ $$ Answered by mind is power last updated on 21/Jan/20 $${y}={x}^{{a}}…
Question Number 13316 by 433 last updated on 18/May/17 $$\begin{cases}{{x}'\left({t}\right)=\mathrm{4}{x}\left({t}\right)+\mathrm{5}{y}\left({t}\right)}\\{{y}'\left({t}\right)=\mathrm{4}{y}\left({t}\right)}\end{cases} \\ $$ Answered by ajfour last updated on 18/May/17 $${dy}=\mathrm{4}{ydt}\:\:\:\:\: \\ $$$$\int\frac{{dy}}{{y}}=\mathrm{4}\int{dt} \\ $$$$\mathrm{ln}\:\left(\frac{{y}}{{y}_{\mathrm{0}} }\right)=\mathrm{4}{t}\:\:\:\:{or}\:\:\boldsymbol{{y}}=\boldsymbol{{y}}_{\mathrm{0}}…
Question Number 144356 by Ar Brandon last updated on 24/Jun/21 $$\mathrm{y}'+\mathrm{cos}\left(\mathrm{x}\right)\mathrm{y}=\mathrm{cos}^{\mathrm{2}} \mathrm{x} \\ $$ Answered by Olaf_Thorendsen last updated on 24/Jun/21 $${y}'+\mathrm{cos}\left({x}\right){y}\:=\:\mathrm{cos}^{\mathrm{2}} {x}\:\:\:\left(\mathrm{1}\right) \\ $$$${y}\:=\:{e}^{−\mathrm{sin}{x}}…
Question Number 13025 by ARJUN SUBBA last updated on 11/May/17 Commented by prakash jain last updated on 13/May/17 $$\mathrm{A}\:\mathrm{should}\:\mathrm{be}\:−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by prakash jain…
Question Number 131488 by Ahmed1hamouda last updated on 05/Feb/21 Answered by Ñï= last updated on 18/Feb/21 $${y}''+\mathrm{2}{y}'+\mathrm{5}{y}=\mathrm{6}{e}^{\mathrm{2}{x}} +{xsin}^{\mathrm{2}} {x}+{e}^{{x}} {cos}\mathrm{2}{x} \\ $$$${y}_{{p}} =\frac{\mathrm{1}}{{D}^{\mathrm{2}} +\mathrm{2}{D}+\mathrm{5}}\left(\mathrm{6}{e}^{\mathrm{2}{x}} +{xsin}^{\mathrm{2}}…