Question Number 127783 by bemath last updated on 02/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:−\frac{\mathrm{y}}{\mathrm{x}}\:=\:\frac{\mathrm{y}^{\mathrm{3}} .\mathrm{e}^{\mathrm{x}} }{\mathrm{x}^{\mathrm{2}} }\: \\ $$ Answered by liberty last updated on 02/Jan/21 $$\:\mathrm{Bernoulli}\:\mathrm{diff}\:\mathrm{equation}\:. \\ $$$$\:\mathrm{let}\:\mathrm{v}\:=\:\mathrm{y}^{−\mathrm{2}}…
Question Number 127780 by bemath last updated on 02/Jan/21 $$\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{2x}\right)\:\mathrm{dy}−\mathrm{2y}\:\mathrm{dx}\:=\:\mathrm{0} \\ $$$$\:\mathrm{y}\left(\mathrm{0}\right)\:=\:\mathrm{1} \\ $$ Answered by liberty last updated on 02/Jan/21 $$\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{2y}}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}}…
Question Number 127781 by shaker last updated on 02/Jan/21 Answered by bemath last updated on 02/Jan/21 $$\begin{cases}{\mathrm{2sin}\:\mathrm{xcos}\:\mathrm{y}=−\mathrm{1}}\\{\mathrm{2cos}\:\mathrm{xsin}\:\mathrm{y}=\mathrm{1}}\end{cases} \\ $$$$\Rightarrow\mathrm{sin}\:\left(\mathrm{x}+\mathrm{y}\right)+\mathrm{sin}\:\left(\mathrm{x}−\mathrm{y}\right)=−\mathrm{1} \\ $$$$\Rightarrow\mathrm{sin}\:\left(\mathrm{x}+\mathrm{y}\right)−\mathrm{sin}\:\left(\mathrm{x}−\mathrm{y}\right)=\mathrm{1} \\ $$$$\Leftrightarrow\:\mathrm{2sin}\:\left(\mathrm{x}+\mathrm{y}\right)=\mathrm{0}\:\Rightarrow\mathrm{sin}\:\left(\mathrm{x}+\mathrm{y}\right)=\mathrm{0} \\ $$$$\:\Rightarrow\mathrm{x}+\mathrm{y}\:=\:\mathrm{n}\pi\:;\:\mathrm{n}\in\mathbb{Z}\:…
Question Number 62244 by Rasheed.Sindhi last updated on 18/Jun/19 $$\mathrm{Find}\:\mathrm{out}\:\mathrm{x},\mathrm{y},\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\mathrm{gcd}\left(\mathrm{x}^{\mathrm{3}} ,\mathrm{y}^{\mathrm{2}} \right)=\mathrm{gcd}\left(\mathrm{x}^{\mathrm{2}} ,\mathrm{y}^{\mathrm{3}} \right) \\ $$ Commented by mr W last updated on…
Question Number 127778 by Bird last updated on 02/Jan/21 $${study}\:{tbe}\:{convergence}\:{of} \\ $$$$\sum_{{n}} ^{\infty} \frac{\mathrm{1}}{{nln}\left(\mathrm{1}+{n}\right)} \\ $$ Answered by mnjuly1970 last updated on 02/Jan/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 127779 by Bird last updated on 02/Jan/21 $${find}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{+\infty} \frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{{n}} } \\ $$ Answered by Dwaipayan Shikari last updated on 02/Jan/21…
Question Number 62242 by Rasheed.Sindhi last updated on 18/Jun/19 $$\mathrm{Find}\:\mathrm{out}\:\mathrm{x},\mathrm{y}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{lcm}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{180}\:\wedge\:\mathrm{gcd}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{45} \\ $$ Commented by maxmathsup by imad last updated on 19/Jun/19 $$\Delta\left({x},{y}\right)\:=\mathrm{45}\:{and}\:{M}\left({x},{y}\right)=\mathrm{180}\:\Rightarrow{x}\:=\mathrm{45}\:{u}\:\:{and}\:{y}\:=\mathrm{45}\:{v}\:{with}\:\Delta\left({u},{v}\right)=\mathrm{1} \\…
Question Number 127776 by Bird last updated on 02/Jan/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{lnx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62241 by vishnurajput8081@gmail.com last updated on 18/Jun/19 $$\boldsymbol{{if}}\:\boldsymbol{{the}}\:\boldsymbol{{point}}\:{A}\:{B}\:{C}\:{with}\:{position}\:{vector}\: \\ $$$$\left(\mathrm{20}\hat {{i}}+\lambda\hat {{j}}\right)\:\left(\mathrm{5}\hat {{i}}−\hat {{j}}\right)\:{and}\left(\mathrm{10}\hat {{i}}−\mathrm{13}\hat {{j}}\right)\:{are} \\ $$$${collinear}\:{then}\:{the}\:{value}\:{of}\:\lambda\:{is}: \\ $$ Answered by tanmay…
Question Number 127777 by Bird last updated on 02/Jan/21 $${explicite}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{lnx}}{{x}^{\mathrm{2}} −{x}+{a}}{dx} \\ $$$${with}\:\:\:{a}>\frac{\mathrm{1}}{\mathrm{4}} \\ $$ Answered by mathmax by abdo last updated on…