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Category: Differential Equation

y-y-3y-2x-

Question Number 126122 by benjo_mathlover last updated on 17/Dec/20 $$\:\:{y}.{y}'+\mathrm{3}{y}=\mathrm{2}{x}\: \\ $$ Answered by Dwaipayan Shikari last updated on 17/Dec/20 $${y}'+\mathrm{3}=\frac{\mathrm{2}{x}}{{y}}\:\:\:\:\:\:\:\:{y}={vx}\Rightarrow{y}'={v}+{xv}' \\ $$$$\Rightarrow{xv}'+{v}+\mathrm{3}=\frac{\mathrm{2}}{{v}}\Rightarrow{xv}'=\frac{\mathrm{2}−{v}^{\mathrm{2}} −\mathrm{3}{v}}{{v}} \\…

If-a-and-b-arbitary-constants-find-a-second-order-equation-which-has-y-ae-x-b-cos-x-as-a-general-solution-

Question Number 125991 by bramlexs22 last updated on 16/Dec/20 $${If}\:{a}\:{and}\:{b}\:{arbitary}\:{constants},\: \\ $$$${find}\:{a}\:{second}\:−\:{order}\:{equation} \\ $$$${which}\:{has}\:{y}\:=\:{ae}^{{x}} +{b}\:\mathrm{cos}\:{x}\:{as}\:{a} \\ $$$${general}\:{solution}. \\ $$ Answered by liberty last updated on…

y-dx-x-ln-x-ln-y-1-dy-0-where-y-1-0-

Question Number 125958 by bramlexs22 last updated on 15/Dec/20 $$\:\:\:\:{y}\:{dx}\:+{x}\left(\mathrm{ln}\:{x}\:−\mathrm{ln}\:{y}−\mathrm{1}\right){dy}=\mathrm{0} \\ $$$$\:\:\:\:{where}\:{y}\left(\mathrm{1}\right)=\mathrm{0} \\ $$ Answered by Olaf last updated on 16/Dec/20 $${ydx}+{x}\left(\mathrm{ln}{x}−\mathrm{ln}{y}−\mathrm{1}\right){dy}\:=\:\mathrm{0} \\ $$$$\mathrm{Let}\:{y}\:=\:{xu} \\…