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Category: Differential Equation

Solve-x-sin-y-dx-x-2-y-cos-y-dy-0-subject-to-y-1-

Question Number 18800 by tawa tawa last updated on 29/Jul/17 $$\mathrm{Solve}:\:\:\mathrm{x}\:\mathrm{sin}\left(\mathrm{y}\right)\mathrm{dx}\:+\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}\:\mathrm{cos}\left(\mathrm{y}\right)\mathrm{dy}\:=\:\mathrm{0},\:\:\mathrm{subject}\:\mathrm{to}\:\mathrm{y}\left(\mathrm{1}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Solve-the-following-differential-equation-d-2-y-dx-2-x-1-x-2-dy-dx-y-1-x-2-x-1-x-2-

Question Number 84232 by niroj last updated on 10/Mar/20 $$\:\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}}. \\ $$$$\:\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:+\:\frac{\boldsymbol{\mathrm{x}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\:\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}−\:\frac{\boldsymbol{\mathrm{y}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }=\:\boldsymbol{\mathrm{x}}\sqrt{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \\ $$ Commented by mind is power last…

Question-149757

Question Number 149757 by iloveisrael last updated on 07/Aug/21 Commented by amin96 last updated on 07/Aug/21 $${x}\frac{{dy}}{{dx}}+\mathrm{2}{y}=\frac{{sinx}}{{x}}\:\:\:\:\:\:\frac{{dy}}{{dx}}=\frac{\mathrm{sin}\:{x}−\mathrm{2}{xy}}{{x}^{\mathrm{2}} } \\ $$$$\left(\mathrm{sin}\:{x}−\mathrm{2}{xy}\right){dx}+\left(−{x}^{\mathrm{2}} \right){dy}=\mathrm{0} \\ $$$$\frac{\partial{M}}{\partial{y}}=−\mathrm{2}{x}\:\:\:\:\:\:\:\frac{\partial{N}}{\partial{x}}=−\mathrm{2}{x}\:\:\:\:\:\:{M}_{{y}} ={N}_{{x}} \:\:\:…

y-2x-3y-1-2-find-the-solution-

Question Number 84212 by jagoll last updated on 10/Mar/20 $$\mathrm{y}'\:=\:\left(\mathrm{2x}+\mathrm{3y}+\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\: \\ $$ Commented by niroj last updated on 10/Mar/20 $$\:\:\frac{\mathrm{dy}}{\mathrm{dx}}=\:\left(\mathrm{2x}+\mathrm{3y}+\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\:\mathrm{put},\:\:\mathrm{2x}+\mathrm{3y}+\mathrm{1}=\mathrm{v} \\…

Show-that-the-differetial-equation-is-a-Sturm-Louville-equation-x-1-y-1-1-4-x-3-y-0-y-1-0-y-t-0-Solve-the-equation-to-determine-the-eigenvalue-and-the-corresponding-eigen-functions

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}.…