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Category: Differential Equation

the-curve-y-3x-2-4-x-2-and-x-3-is-rotated-about-the-x-axis-find-the-volume-of-the-solid-generated-Leave-your-answer-in-terms-of-pi-

Question Number 47510 by Rio Michael last updated on 11/Nov/18 $${the}\:{curve}\:{y}\:=\:\mathrm{3}{x}^{\mathrm{2}} \:+\mathrm{4}\:\left({x}=\mathrm{2}\:{and}\:{x}=\mathrm{3}\right)\:{is}\:{rotated}\:{about}\:{the}\: \\ $$$${x}.{axis}.{find}\:{the}\:{volume}\:{of}\:{the}\:{solid}\:{generated}.{Leave}\:{your} \\ $$$${answer}\:{in}\:{terms}\:{of}\:\pi. \\ $$ Commented by mr W last updated on…

Find-general-solution-1-sin-x-1-y-dy-dx-cos-x-2-X-tan-1-2-11-cot-1-24-7-tan-1-1-3-find-X-

Question Number 112844 by bemath last updated on 10/Sep/20 $$\:\mathrm{Find}\:\mathrm{general}\:\mathrm{solution} \\ $$$$\left(\mathrm{1}\right)\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{1}+\mathrm{y}}\right)\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{cos}\:\mathrm{x} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{X}\:=\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\mathrm{11}}\right)+\mathrm{cot}^{−\mathrm{1}} \left(\frac{\mathrm{24}}{\mathrm{7}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{3}}\right) \\ $$$$\:\:\mathrm{find}\:\mathrm{X}\:. \\ $$ Commented by bemath last…

solve-dy-dx-4y-x-1-2-x-

Question Number 112456 by bobhans last updated on 08/Sep/20 $$\mathrm{solve}\:\frac{\mathrm{dy}}{\mathrm{dx}}−\frac{\mathrm{4y}}{\mathrm{x}}\:=\:\mathrm{1}+\frac{\mathrm{2}}{\mathrm{x}} \\ $$ Answered by john santu last updated on 08/Sep/20 $${let}\:{u}\:=\:{yx}^{−\mathrm{4}} \:\rightarrow\frac{{du}}{{dx}}\:=\:−\mathrm{4}{yx}^{−\mathrm{5}} +{x}^{−\mathrm{4}} \:\frac{{dy}}{{dx}} \\…

y-y-y-2-e-y-y-y-2-not-sure-if-it-s-possible-to-solve-this-at-all-

Question Number 46694 by MJS last updated on 30/Oct/18 $$\left({y}''{y}−\left({y}'\right)^{\mathrm{2}} \right)\mathrm{e}^{\frac{{y}'}{{y}}} ={y}^{\mathrm{2}} \\ $$$$\mathrm{not}\:\mathrm{sure}\:\mathrm{if}\:\mathrm{it}'\mathrm{s}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{at}\:\mathrm{all}… \\ $$ Answered by ajfour last updated on 30/Oct/18 $$\mathrm{ln}\:\left[{y}''{y}−\left({y}'\right)^{\mathrm{2}} \right]+\frac{{y}'}{{y}}=\mathrm{2ln}\:{y}…