Question Number 124634 by bemath last updated on 05/Dec/20 $$\:{Solve}\:{the}\:{equation}\:\frac{\partial^{\mathrm{2}} {z}}{\partial{x}\partial{y}}\:=\:{x}^{\mathrm{2}} {y} \\ $$$$\left(\mathrm{1}\right)\:{particular}\:{solution}\:{which}\: \\ $$$$\:{z}\left({x},\mathrm{0}\right)\:=\:{x}^{\mathrm{2}} \:{and}\:{z}\left(\mathrm{1},{y}\right)=\mathrm{cos}\:{y} \\ $$$$ \\ $$ Answered by liberty last…
Question Number 124619 by arkanmath7@gmail.com last updated on 04/Dec/20 $${find}\:{the}\:{inverse}\:{of}\:{y}={x}^{\mathrm{4}} −\mathrm{2}\boldsymbol{{x}}+\mathrm{1} \\ $$ Commented by MJS_new last updated on 04/Dec/20 $${x}^{\mathrm{4}} −\mathrm{2}{x}−\left({y}+\mathrm{1}\right)=\mathrm{0} \\ $$$${x}=? \\…
Question Number 59037 by Rdk96 last updated on 03/May/19 $${solve}\:\:\frac{{dy}}{{dt}}={t}^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$ Commented by tanmay last updated on 04/May/19 $${unique}\:{problem}\:…{still}\:{trying}\:{to}\:{find}\:{the}\:{way} \\ $$$${to}\:{proceed}\:{further}… \\ $$…
Question Number 124389 by Engr_Jidda last updated on 03/Dec/20 Answered by Dwaipayan Shikari last updated on 03/Dec/20 $$\int_{\mathrm{0}} ^{\infty} {x}^{{m}} {e}^{−{ax}^{{n}} } {dx}\:\:\:\:\:\:\:{ax}^{{n}} ={u}\Rightarrow{anx}^{{n}−\mathrm{1}} =\frac{{du}}{{dx}}…
Question Number 124050 by john_santu last updated on 30/Nov/20 $$\left(\mathrm{6}{x}+{y}^{\mathrm{2}} \right){dx}\:+{y}\left(\mathrm{2}{xy}−\mathrm{3}{y}^{\mathrm{2}} \right){dy}\:=\:\mathrm{0}\: \\ $$ Answered by mohammad17 last updated on 30/Nov/20 $${M}=\mathrm{6}{x}+{y}^{\mathrm{2}} \rightarrow{M}_{{y}} =\mathrm{2}{y}\rightarrow\left(\ast\right) \\…
Question Number 123982 by Ar Brandon last updated on 29/Nov/20 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{D}.\mathrm{E}\:\left(\mathrm{E}\right):\:\mathrm{x}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\mathrm{y}'−\mathrm{2y}=\mathrm{x}^{\mathrm{3}} \left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} \mathrm{e}^{−\mathrm{x}} \\ $$$$\mathrm{a}\backslash\:\mathrm{Resolve}\:\mathrm{the}\:\mathrm{DE}\:\mathrm{x}\left(\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)\mathrm{y}'−\mathrm{2y}=\mathrm{0} \\ $$$$\mathrm{b}\backslash\mathrm{We}\:\mathrm{wish}\:\mathrm{to}\:\mathrm{find}\:\mathrm{a}\:\mathrm{function}\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{h}\left(\mathrm{x}\right)\:\mathrm{defined}\:\mathrm{by}\:\mathrm{h}\left(\mathrm{x}\right)=\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{g}\left(\mathrm{x}\right) \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{particular}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\left(\mathrm{E}\right)…
Question Number 123983 by Ar Brandon last updated on 29/Nov/20 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{real}\:\mathrm{number}\:\mathrm{c}\:\mathrm{and}\:\mathrm{the}\:\mathrm{DE}\:\left(\mathrm{H}\right)\:\mathrm{below} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}''+\mathrm{2y}'+\mathrm{cy}=\mathrm{0} \\ $$$$\mathrm{a}\backslash\mathrm{Given}\:\mathrm{c}=\mathrm{3}.\:\mathrm{Rewrite}\:\mathrm{and}\:\mathrm{resolve}\:\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\mathrm{the}\:\mathrm{equation}\:\left(\mathrm{H}\right) \\ $$$$\mathrm{b}\backslash\mathrm{for}\:\mathrm{c}=\mathrm{1},\:\mathrm{Rewrite}\:\mathrm{and}\:\mathrm{resolve}\:\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\mathrm{the}\:\mathrm{equation}\:\left(\mathrm{H}\right) \\ $$$$\mathrm{c}\backslash\mathrm{for}\:\mathrm{c}=\mathrm{10}; \\ $$$$\:\:\:\:\mathrm{i}.\:\mathrm{Rewrite}\:\mathrm{and}\:\mathrm{resolve}\:\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\mathrm{the}\:\mathrm{equation}\:\left(\mathrm{H}\right) \\ $$$$\:\:\:\mathrm{ii}.\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{limit}\:\mathrm{at}\:+\infty\:\mathrm{of}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{this}\:\mathrm{DE}. \\ $$$$\:\:\mathrm{iii}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{verifying}\:\mathrm{the}\:\mathrm{initial}\:\mathrm{conditions}:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{0}…
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Question Number 123858 by Dwaipayan Shikari last updated on 28/Nov/20 $$\overset{..} {\theta}+\frac{{g}}{{l}}{sin}\theta=\mathrm{0}\:\:\:\:\:\left({Find}\:{the}\:{exact}\:{solution}\right) \\ $$ Answered by Olaf last updated on 29/Nov/20 $$\overset{\bullet\bullet} {\theta}+\frac{{g}}{{l}}\mathrm{sin}\theta\:=\:\mathrm{0}\:\left(\mathrm{1}\right) \\ $$$$\left(\mathrm{1}\right)×\overset{\bullet}…
Question Number 123716 by Engr_Jidda last updated on 02/Jan/21 Commented by Dwaipayan Shikari last updated on 27/Nov/20 $${What}\:{is}\:{B}_{{n}} \:{here}? \\ $$ Commented by Engr_Jidda last…