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Category: Differential Equation

d-2-y-dx-2-tan-x-dy-dx-0-

Question Number 175406 by princeDera last updated on 29/Aug/22 $$\frac{{d}^{\mathrm{2}} \boldsymbol{{y}}}{\boldsymbol{{dx}}^{\mathrm{2}} }\:−\mathrm{tan}\:\left(\boldsymbol{{x}}\right)\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}}\:=\:\mathrm{0} \\ $$ Answered by Ar Brandon last updated on 29/Aug/22 $${y}''−\mathrm{tan}{x}\centerdot{y}'=\mathrm{0} \\ $$$$\Rightarrow\frac{{y}''}{{y}'}=\mathrm{tan}{x}…

Solve-x-2-y-xy-y-x-y-1-x-

Question Number 43616 by Tawa1 last updated on 12/Sep/18 $$\mathrm{Solve}:\:\:\:\mathrm{x}^{\mathrm{2}} \mathrm{y}''\:\:+\:\:\mathrm{xy}'\:\:−\:\mathrm{y}\:=\:\mathrm{x}\:,\:\:\:\:\:\:\:\:\mathrm{y}_{\mathrm{1}} \:=\:\mathrm{x} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 13/Sep/18 $${x}={e}^{{t}} \:\:\:\frac{{dx}}{{dt}}={e}^{{t}} \\ $$$$\frac{{dy}}{{dx}}=\frac{{dy}}{{dt}}×\frac{{dt}}{{dx}}=\frac{{dy}}{{dt}}×\frac{\mathrm{1}}{{e}^{{t}}…

1-2x-y-4x-2-y-8y-0-

Question Number 108491 by Ar Brandon last updated on 17/Aug/20 $$\left(\mathrm{1}+\mathrm{2x}\right)\mathrm{y}''+\left(\mathrm{4x}−\mathrm{2}\right)\mathrm{y}'−\mathrm{8y}=\mathrm{0} \\ $$ Answered by Ar Brandon last updated on 20/Aug/20 $$\mathrm{6}.\:\left(\mathrm{1}+\mathrm{2x}\right)\mathrm{y}''+\left(\mathrm{4x}−\mathrm{2}\right)\mathrm{y}'−\mathrm{8y}=\mathrm{0} \\ $$$$\Rightarrow\left(\mathrm{2x}+\mathrm{1}\right)\left(\mathrm{y}''+\mathrm{2y}'\right)+\mathrm{4}\left(\mathrm{y}'+\mathrm{2y}\right)=\mathrm{0} \\…