Question Number 84085 by M±th+et£s last updated on 09/Mar/20 $${solve} \\ $$$$\frac{{d}}{{dr}}\left({r}\frac{{d}\theta}{{dr}}\right)=\mathrm{0} \\ $$ Answered by TANMAY PANACEA last updated on 09/Mar/20 $$\frac{{d}}{{dr}}\left({r}\frac{{d}\theta}{{dr}}\right)=\mathrm{0}=\frac{{dA}}{{dr}}\:\:{A}={constant} \\ $$$${r}\frac{{d}\theta}{{dr}}={A}…
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Question Number 83619 by Jidda28 last updated on 04/Mar/20 $${Show}\:{that}\:{the}\:{differetial}\:{equation}\:{is}\:{a}\:{Sturm}−{Louville}\:{equation} \\ $$$$\left({x}^{−\mathrm{1}} {y}^{\mathrm{1}} \right)^{\mathrm{1}} +\left(\mathrm{4}+\lambda\right){x}^{−\mathrm{3}} {y}=\mathrm{0},\:\:{y}\left(\mathrm{1}\right)=\mathrm{0},{y}\left(\varrho^{{t}} \right)=\mathrm{0} \\ $$$${Solve}\:{the}\:{equation}\:{to}\:{determine}\:{the}\:{eigenvalue}\:{and}\:{the}\:{corresponding}\:{eigen}\:{functions}\:{of}\:{the}\:{problem}. \\ $$$${Show}\:{also}\:{that}\:{the}\:{set}\:{of}\:{eigen}\:{function}\:{forms}\:{and}\:{orthogonal}\:{and}\:{orthonormal}\:{set}. \\ $$$$ \\ $$$${Thanks}\:{as}\:{usual}.…
Question Number 83565 by Jidda28 last updated on 03/Mar/20 Commented by abdomathmax last updated on 04/Mar/20 $${I}=\int_{−\infty} ^{+\infty} \:\frac{{e}^{\mathrm{2}{x}} }{{e}^{\mathrm{3}{x}} \:+\mathrm{1}}{dx}\:{changement}\:{e}^{{x}} ={t}\:{give} \\ $$$${I}\:\:=\int_{\mathrm{0}} ^{+\infty}…
Question Number 83558 by Jidda28 last updated on 03/Mar/20 Commented by Jidda28 last updated on 03/Mar/20 $${help}\:{me}\:{out}\:{pls}. \\ $$ Commented by mathmax by abdo last…
Question Number 83559 by Jidda28 last updated on 03/Mar/20 Commented by Jidda28 last updated on 03/Mar/20 $${help}\:{me}\:{out}\:{pls}. \\ $$ Answered by mind is power last…
Question Number 83327 by john santu last updated on 01/Mar/20 $$\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:−\mathrm{2x}\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\mathrm{p}\left(\mathrm{p}+\mathrm{1}\right)\mathrm{y}\:=\:\mathrm{0}\: \\ $$$$\mathrm{in}\:\mathrm{descending}\:\mathrm{power}\:\mathrm{of}\:\mathrm{x}.\:\mathrm{what}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{solution}? \\ $$ Commented by Joel578 last updated…
Question Number 17735 by tawa tawa last updated on 09/Jul/17 $$\mathrm{Solve}:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\mathrm{ysec}\left(\mathrm{x}\right)\:=\:\mathrm{tan}\left(\mathrm{x}\right) \\ $$ Answered by alex041103 last updated on 10/Jul/17 $$\mathrm{So}\:\mathrm{let}'\mathrm{s}\:\mathrm{find}\:\mathrm{function}\:\mu\left(\mathrm{x}\right)\:\mathrm{wich}\:\mathrm{satisfies}\:\mathrm{the}\:\mathrm{followinv} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\mu+\mathrm{P}\left(\mathrm{x}\right)\mu\mathrm{y}=\frac{\mathrm{d}}{\mathrm{dx}}\left[\mathrm{y}\mu\right] \\ $$$$\mathrm{We}\:\mathrm{know}\:\mathrm{that}…
Question Number 17734 by tawa tawa last updated on 09/Jul/17 $$\mathrm{If}\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{3}} \:−\:\mathrm{3xy}\:=\:\mathrm{0}, \\ $$$$\mathrm{Show}\:\mathrm{that},\:\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:=\:\frac{−\:\mathrm{2xy}}{\mathrm{y}^{\mathrm{2}} \:−\:\mathrm{x}^{\mathrm{2}} } \\ $$ Terms of Service Privacy…
Question Number 83159 by jagoll last updated on 28/Feb/20 $$\mathrm{3x}\:\left(\mathrm{xy}−\mathrm{2}\right)\mathrm{dx}\:+\:\left(\mathrm{x}^{\mathrm{3}} +\mathrm{2y}\right)\:\mathrm{dy}\:=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution} \\ $$ Commented by niroj last updated on 28/Feb/20 $$\:\:\:\left(\mathrm{3x}^{\mathrm{2}} \mathrm{y}−\mathrm{6x}\right)\mathrm{dx}+\left(\mathrm{x}^{\mathrm{3}} +\mathrm{2y}\right)\mathrm{dy}=\mathrm{0}…