Menu Close

Category: Differential Equation

y-y-sec-x-

Question Number 153542 by EDWIN88 last updated on 08/Sep/21 $$\:{y}'''+{y}'=\mathrm{sec}\:{x}\: \\ $$ Answered by puissant last updated on 08/Sep/21 $${y}'''+{y}'={secx} \\ $$$$\Rightarrow\:{y}''+{y}={ln}\left({tan}\left(\frac{{x}}{\mathrm{2}}+\frac{\pi}{\mathrm{2}}\right)\right)+{C}_{\mathrm{1}} \\ $$$$\Rightarrow\:\left({D}^{\mathrm{2}} +{D}\right){y}={ln}\left({tan}\left(\frac{{x}}{\mathrm{2}}+\frac{\pi}{\mathrm{2}}\right)\right)+{C}_{\mathrm{1}}…

y-3y-2y-10sin-x-2cos-2x-

Question Number 87904 by john santu last updated on 07/Apr/20 $$\mathrm{y}\:''\:−\mathrm{3y}'\:+\mathrm{2y}\:=\:\mathrm{10sin}\:\mathrm{x}\:+\:\mathrm{2cos}\:\mathrm{2x} \\ $$ Commented by niroj last updated on 07/Apr/20 $$\:\:\mathrm{y}^{''} −\mathrm{3y}^{'} +\mathrm{2y}=\mathrm{10sin}\:\mathrm{x}+\mathrm{2cos}\:\mathrm{2x} \\ $$$$\:\:\:\left(\mathrm{D}^{\mathrm{2}}…

prove-x-1-x-n-y-1-y-n-R-x-1-x-2-x-n-y-1-y-2-y-n-x-1-y-1-x-2-y-2-x-n-y-n-

Question Number 21252 by youssoufab last updated on 17/Sep/17 $${prove},\forall{x}_{\mathrm{1}} ,…,{x}_{{n}} {y}_{\mathrm{1}} ,…,{y}_{{n}} \in\mathbb{R}^{+} \\ $$$$\sqrt{{x}_{\mathrm{1}} {x}_{\mathrm{2}} …{x}_{{n}} }+\sqrt{{y}_{\mathrm{1}} {y}_{\mathrm{2}} …{y}_{{n}} }\leqslant\sqrt{\left({x}_{\mathrm{1}} +{y}_{\mathrm{1}} \right)\left({x}_{\mathrm{2}} +{y}_{\mathrm{2}}…