Question Number 168267 by Florian last updated on 07/Apr/22 $$\:\:\:\:\:\:{Solve}\:\:{this}\:{integral}\:: \\ $$$$\:\:\:\:\:\:\:\int\frac{\sqrt{{x}+\mathrm{1}}−\mathrm{1}}{\:\sqrt{{x}+\mathrm{1}}+\mathrm{1}} \\ $$$$ \\ $$ Answered by MJS_new last updated on 07/Apr/22 $$\int\frac{\sqrt{{x}+\mathrm{1}}−\mathrm{1}}{\:\sqrt{{x}+\mathrm{1}}+\mathrm{1}}{dx}= \\…
Question Number 102716 by Ar Brandon last updated on 10/Jul/20 $$\mathrm{y}''+\mathrm{3y}'−\mathrm{10y}=\mathrm{14e}^{−\mathrm{5x}} \\ $$ Answered by bramlex last updated on 10/Jul/20 $$\mathrm{Homogenous}\: \\ $$$$\mathrm{r}^{\mathrm{2}} +\mathrm{3r}−\mathrm{10}=\mathrm{0}\:\Rightarrow\left(\mathrm{r}+\mathrm{5}\right)\left(\mathrm{r}−\mathrm{2}\right)=\mathrm{0} \\…
Question Number 102639 by bobhans last updated on 10/Jul/20 $$\frac{{dy}}{{dx}}\:−\mathrm{2}{xy}\:=\:\mathrm{6}{y}\:{e}^{{y}^{\mathrm{2}} } \\ $$ Answered by Ar Brandon last updated on 10/Jul/20 $$\mathrm{Let}\:\mathrm{y}=\mathrm{vx}\:\Rightarrow\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{v}+\mathrm{x}\frac{\mathrm{dv}}{\mathrm{dx}} \\ $$$$\Rightarrow\:\mathrm{v}+\mathrm{x}\frac{\mathrm{dv}}{\mathrm{dx}}−\mathrm{2vx}^{\mathrm{2}} =\mathrm{6vxe}^{\mathrm{v}^{\mathrm{2}}…
Question Number 102527 by bemath last updated on 09/Jul/20 $$\mathrm{2}{y}''−{y}'+{y}\:=\:\mathrm{cos}\:\mathrm{3}{x}\: \\ $$ Answered by Ar Brandon last updated on 09/Jul/20 $$\mathrm{Let}\:\mathrm{y}=\mathrm{acos3x}+\mathrm{bsin3x} \\ $$$$\Rightarrow\mathrm{y}'=−\mathrm{3asin3x}+\mathrm{3bcos3x}\:,\:\mathrm{y}''=−\mathrm{9acos3x}−\mathrm{9bsin3x} \\ $$$$\Rightarrow−\mathrm{2}×\mathrm{9}\left(\mathrm{acos3x}+\mathrm{bsin3x}\right)−\mathrm{3}\left(\mathrm{bcos3x}−\mathrm{asin3x}\right)+\mathrm{acos3x}+\mathrm{bsin3x}…
Question Number 102515 by bemath last updated on 09/Jul/20 $$\left(\frac{{x}}{{y}}\right){y}'=\:\frac{\mathrm{2}{y}^{\mathrm{2}} +\mathrm{1}}{{x}+\mathrm{1}} \\ $$ Answered by bobhans last updated on 09/Jul/20 $$\frac{{dy}}{{y}\left(\mathrm{2}{y}^{\mathrm{2}} +\mathrm{1}\right)}\:=\:\frac{{dx}}{{x}\left({x}+\mathrm{1}\right)} \\ $$$$\left(\mathrm{1}\right)\:\frac{\mathrm{1}}{{y}\left(\mathrm{2}{y}^{\mathrm{2}} +\mathrm{1}\right)}\:=\:\frac{{A}}{{y}}\:+\:\frac{{By}+{C}}{\mathrm{2}{y}^{\mathrm{2}}…
Question Number 102517 by bemath last updated on 09/Jul/20 $$\left(\mathrm{1}+{x}^{\mathrm{2}} \right){dy}\:+\:\left(\mathrm{1}+{y}^{\mathrm{2}} \right){dx}\:=\:\mathrm{0} \\ $$ Commented by bemath last updated on 09/Jul/20 Terms of Service Privacy…
Question Number 168011 by Mastermind last updated on 31/Mar/22 $${Solve}\: \\ $$$$\left(\mathrm{2}{x}+\mathrm{5}{y}+\mathrm{1}\right){dx}\:−\:\left(\mathrm{5}{x}+\mathrm{2}{y}−\mathrm{1}\right){dy}=\mathrm{0} \\ $$$$ \\ $$$${Mastermind} \\ $$ Answered by mr W last updated on…
Question Number 102382 by Ar Brandon last updated on 08/Jul/20 $$\mathrm{x}^{\mathrm{2}} \centerdot\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{x}^{\mathrm{2}} +\mathrm{xy}+\mathrm{y}^{\mathrm{2}} \\ $$ Answered by PRITHWISH SEN 2 last updated on 08/Jul/20 $$\mathrm{put}\:\mathrm{y}=\mathrm{vx}…
Question Number 167917 by guddupari last updated on 29/Mar/22 $$\:_{} \: \\ $$$$\mathrm{Two}\:\mathrm{small}\:\mathrm{charged}\:\mathrm{spheresn} \\ $$$$\mathrm{Two}\:\mathrm{small}\:\mathrm{charged}\:\mathrm{spheresn} \\ $$$$\mathrm{cotain}\:\mathrm{charges}\:+\:\mathrm{q1}\:\mathrm{and}\:+\:\mathrm{q2r} \\ $$$$\mathrm{espectively}.\:\mathrm{A}\:\mathrm{charge}\:\mathrm{da}\:\mathrm{ism} \\ $$$$\mathrm{reoved}\:\mathrm{from}\:\mathrm{sphere}\:\mathrm{carryingh} \\ $$$$\mathrm{carge}\:\mathrm{q1}\:\mathrm{and}\:\mathrm{is}\:\mathrm{transferredtoh} \\ $$$$\mathrm{te}\:\mathrm{other}.\:\mathrm{Find}\:\mathrm{charge}\:\mathrm{on}\:\mathrm{eachs}…
Question Number 102298 by Ar Brandon last updated on 08/Jul/20 $$\mathrm{sinx}\centerdot\frac{\mathrm{dy}}{\mathrm{dx}}−\mathrm{ycosx}=\mathrm{y}^{\mathrm{3}} \mathrm{sin}^{\mathrm{2}} \mathrm{xcosx} \\ $$ Answered by john santu last updated on 08/Jul/20 $$\frac{{dy}}{{dx}}−{y}\mathrm{cot}\:{x}=\mathrm{sin}\:{x}\mathrm{cos}\:{x}\:.{y}^{\mathrm{3}} \\…