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Author: Tinku Tara

Solve-the-following-D-E-dy-dx-2-2y-2-0-Does-d-2-y-dx-2-2-2y-2-0-have-any-solutions-other-than-y-1-

Question Number 1575 by 112358 last updated on 21/Aug/15 $${Solve}\:{the}\:{following}\:{D}.{E}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} +\mathrm{2}{y}+\mathrm{2}=\mathrm{0}\: \\ $$$${Does}\:\:\left(\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\right)^{\mathrm{2}} +\mathrm{2}{y}+\mathrm{2}=\mathrm{0}\:{have} \\ $$$${any}\:{solutions}\:{other}\:{than} \\ $$$${y}=−\mathrm{1}\:? \\ $$ Commented…

Question-132647

Question Number 132647 by aurpeyz last updated on 15/Feb/21 Answered by Dwaipayan Shikari last updated on 15/Feb/21 $$\int\frac{\mathrm{1}}{\:\sqrt{{x}}\left(\sqrt{{x}}+\mathrm{7}\right)}{dx}\:\:\:\:\:\:\:\:{x}={t}^{\mathrm{2}} \\ $$$$=\mathrm{2}\int\frac{\mathrm{1}}{{t}+\mathrm{7}}{dt}=\mathrm{2}{log}\left({t}+\mathrm{7}\right)+{C}={log}\left(\sqrt{{x}}+\mathrm{7}\right)^{\mathrm{2}} +{C} \\ $$ Answered by…

Three-school-children-share-some-oranges-as-follows-Akwasi-gets-1-3-of-the-total-and-the-remainder-is-shared-between-Abena-and-Juana-in-the-ratio-2-3-If-Abena-gets-24-oranges-how-many-does-Ak

Question Number 67108 by otchereabdullai@gmail.com last updated on 22/Aug/19 $$\mathrm{Three}\:\mathrm{school}\:\mathrm{children}\:\mathrm{share}\:\mathrm{some}\: \\ $$$$\mathrm{oranges}\:\mathrm{as}\:\mathrm{follows}:\:\mathrm{Akwasi}\:\mathrm{gets}\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{total}\:\mathrm{and}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{is}\:\mathrm{shared} \\ $$$$\mathrm{between}\:\mathrm{Abena}\:\mathrm{and}\:\mathrm{Juana}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio} \\ $$$$\mathrm{2}:\:\mathrm{3}\:.\:\mathrm{If}\:\mathrm{Abena}\:\mathrm{gets}\:\mathrm{24}\:\mathrm{oranges}\:,\:\mathrm{how} \\ $$$$\mathrm{many}\:\mathrm{does}\:\mathrm{Akwasi}\:\mathrm{get}. \\ $$ Commented by Prithwish…

lim-0-t-dt-

Question Number 1573 by 123456 last updated on 20/Aug/15 $$\underset{\epsilon\rightarrow+\infty} {\mathrm{lim}}\:\underset{\mathrm{0}} {\overset{\epsilon} {\int}}\epsilon^{−{t}} {dt}=? \\ $$ Commented by 112358 last updated on 21/Aug/15 $${Let}\:{I}\left(\epsilon\right)=\int_{\mathrm{0}} ^{\:\epsilon}…

1-e-x-9e-x-dx-

Question Number 132641 by aurpeyz last updated on 15/Feb/21 $$\int\frac{\mathrm{1}}{{e}^{{x}} +\mathrm{9}{e}^{−{x}} }{dx} \\ $$ Answered by MJS_new last updated on 15/Feb/21 $${t}=\mathrm{e}^{{x}} \:\rightarrow\:{dx}=\frac{{dt}}{{t}} \\ $$$$\int\frac{{dt}}{{t}^{\mathrm{2}}…

find-the-area-abounded-y-x-afind-y-x-2-

Question Number 67106 by mhmd last updated on 22/Aug/19 $${find}\:{the}\:{area}\:{abounded}\:{y}=\sqrt{{x}} \\ $$$${afind}\:{y}={x}−\mathrm{2}? \\ $$ Commented by kaivan.ahmadi last updated on 24/Aug/19 $${x}−\mathrm{2}=\sqrt{{x}}\Rightarrow{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{4}=\mathrm{0}\Rightarrow\left({x}−\mathrm{1}\right)\left({x}−\mathrm{4}\right)=\mathrm{0}\Rightarrow \\ $$$$\begin{cases}{{x}=\mathrm{1}}\\{{x}=\mathrm{2}}\end{cases}…