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Category: Differential Equation

dy-dx-3y-tan-x-1-2-sin-2x-

Question Number 121960 by bemath last updated on 13/Nov/20 $$\:\:\frac{{dy}}{{dx}}\:+\:\mathrm{3}{y}\:\mathrm{tan}\:{x}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{2}{x}\: \\ $$ Answered by liberty last updated on 13/Nov/20 $$\:\mathrm{y}'\:+\:\mathrm{3y}\:\mathrm{tan}\:\mathrm{x}\:=\:\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x} \\ $$$$\:\mathrm{IF}\:\mathrm{u}\:=\:\mathrm{e}^{\int\:\mathrm{3}\:\mathrm{tan}\:\mathrm{x}\:\mathrm{dx}} \:=\:\mathrm{e}^{−\mathrm{3}\int\:\frac{\mathrm{d}\left(\mathrm{cos}\:\mathrm{x}\right)}{\mathrm{cos}\:\mathrm{x}}} =\:\mathrm{e}^{\mathrm{ln}\:\left(\mathrm{sec}\:^{\mathrm{3}} \mathrm{x}\:\right)}…

what-are-the-numerical-coefficients-in-the-quadration-equation-10-2-7-2-0-a-a-10-b-7c-2-b-a-2-b-4-c-2-c-a-2-b-7-c-10-d-a-10-b-7-c-2-

Question Number 121746 by KathleenannLabrador last updated on 11/Nov/20 $${what}\:{are}\:{the}\:{numerical}\:{coefficients}\:{in}\:{the}\:{quadration}\:{equation}\:−\mathrm{10}×\mathrm{2}−\mathrm{7}×+\mathrm{2}=\mathrm{0}?\:\:\:{a}.{a}=\mathrm{10}.{b}=.\mathrm{7}{c}=\mathrm{2}\:\:\:\:\:\:\:\:\:{b}.{a}=−\mathrm{2}.{b}=\mathrm{4}.{c}=−\mathrm{2}\:\:\:\:\:\:\:\:\:\:{c}.{a}=\mathrm{2}.{b}=\mathrm{7}.{c}=\mathrm{10}\:\:\:\:\:\:\:\:{d}.{a}=−\mathrm{10}.{b}=−\mathrm{7}.{c}=\mathrm{2} \\ $$ Answered by MJS_new last updated on 11/Nov/20 $$\mathrm{if}\:\mathrm{you}\:\mathrm{mean} \\ $$$$−\mathrm{10}{x}^{\mathrm{2}} −\mathrm{7}{x}+\mathrm{2}=\mathrm{0} \\ $$$$\mathrm{the}\:\mathrm{answer}\:\mathrm{is}\:\left({d}\right)\:{a}=−\mathrm{10};\:{b}=−\mathrm{7};\:{c}=\mathrm{2}…

Question-121687

Question Number 121687 by abdelsalamalmukasabe last updated on 10/Nov/20 Commented by bemath last updated on 11/Nov/20 $$\left(\frac{\mathrm{2}{y}^{\mathrm{4}} +\mathrm{1}}{{y}^{\mathrm{2}} }\right)\:{dx}\:+\:\left(\mathrm{4}{xy}\right)\:{dy}\:=\:\mathrm{0} \\ $$$$\left(\mathrm{2}{y}^{\mathrm{4}} +\mathrm{1}\right)\:{dx}\:+\:\left(\mathrm{4}{xy}^{\mathrm{3}} \right)\:{dy}\:=\:\mathrm{0} \\ $$$$\Rightarrow\:\frac{{dy}}{{dx}}\:=\:\frac{−\left(\mathrm{2}{y}^{\mathrm{4}}…

Given-implicit-expression-x-tan-y-tan-where-x-y-and-is-variable-Prove-that-dy-dx-1-y-2-1-x-2-0-

Question Number 121633 by liberty last updated on 10/Nov/20 $$\mathrm{Given}\:\mathrm{implicit}\:\mathrm{expression}\:\begin{cases}{\mathrm{x}=\mathrm{tan}\:\alpha}\\{\mathrm{y}=\mathrm{tan}\:\beta}\end{cases} \\ $$$$\mathrm{where}\:\mathrm{x},\mathrm{y},\alpha\:\mathrm{and}\:\beta\:\mathrm{is}\:\mathrm{variable}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\frac{\mathrm{1}+\mathrm{y}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:=\:\mathrm{0}\:. \\ $$ Commented by Dwaipayan Shikari last updated on…

y-y-1-cot-x-y-

Question Number 55939 by MJS last updated on 06/Mar/19 $$\frac{{y}'}{{y}}=\mathrm{1}−\mathrm{cot}\:{x} \\ $$$${y}=? \\ $$ Answered by kaivan.ahmadi last updated on 06/Mar/19 $$\frac{\mathrm{1}}{{y}}\:\frac{{dy}}{{dx}}=\mathrm{1}−{cotx}\Rightarrow \\ $$$$\frac{\mathrm{1}}{{y}}{dy}=\left(\mathrm{1}−{cotx}\right){dx}\Rightarrow \\…

Question-121461

Question Number 121461 by bramlexs22 last updated on 08/Nov/20 Answered by Olaf last updated on 08/Nov/20 $$\left(\mathrm{3}{y}^{\mathrm{2}} +\mathrm{10}{xy}^{\mathrm{2}} \right){dx}+\left(\mathrm{6}{xy}−\mathrm{2}+\mathrm{10}{x}^{\mathrm{2}} {y}\right){dy}\:=\:\mathrm{0} \\ $$$$\mathrm{d}{f}\:=\:\frac{\partial{f}}{\partial{x}}\left({x},{y}\right){dx}+\frac{\partial{f}}{\partial{y}}\left({x},{y}\right){dy}\:=\:\mathrm{0} \\ $$$$ \\…