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Question Number 198646 by Engr_Jidda last updated on 22/Oct/23 Answered by mr W last updated on 23/Oct/23 $${story}\:{is}\:{silly},\:{but}\:{solution}\:{is}\:{easy}! \\ $$$$ \\ $$$${girl}:\:{a}\left({t}\right)=\mathrm{1}×{t}={t} \\ $$$${boy}:\:\:{b}\left({t}\right)=\mathrm{5}×{t}=\mathrm{5}{t} \\…
Question Number 198285 by samiksha last updated on 16/Oct/23 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 198286 by samiksha last updated on 16/Oct/23 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 198104 by sonu753 last updated on 10/Oct/23 Answered by mr W last updated on 11/Oct/23 $$\frac{{dx}}{{dy}}−\frac{{x}}{{y}}=−{y} \\ $$$$\left[{d}.{e}.\:{of}\:{type}\:{y}'+{p}\left({x}\right){y}={q}\left({x}\right)\right] \\ $$$$\int{p}\left({y}\right){dy}=−\int\frac{{dy}}{{y}}=−\mathrm{ln}\:{y} \\ $$$${u}\left({y}\right)={e}^{−\mathrm{ln}\:{y}} =\frac{\mathrm{1}}{{y}}…
Question Number 197389 by uchihayahia last updated on 16/Sep/23 $$ \\ $$$${please}\:{check}\:{my}\:{answer} \\ $$$$\:\left({x}−\mathrm{2}{y}+\mathrm{5}\right){dx}+\left(\mathrm{2}{x}−{y}+\mathrm{4}\right){dy}=\mathrm{0} \\ $$$$\:{X}={x}+{a}\:\&\:{Y}={y}+{b} \\ $$$$ \\ $$$$\:\left({X}−{a}−\mathrm{2}{Y}+\mathrm{2}{b}+\mathrm{5}\right){dX}+\left(\mathrm{2}{X}−\mathrm{2}{a}−{Y}+{b}+\mathrm{4}\right){dY}=\mathrm{0} \\ $$$$\:-{a}+\mathrm{2}{b}=-\mathrm{5} \\ $$$$\:-\mathrm{2}{a}+{b}=-\mathrm{4} \\…
Question Number 197113 by Erico last updated on 08/Sep/23 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:+\infty} \left(\frac{{ln}\left({t}+\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }\right)}{{t}}\right){dt}=\frac{\pi^{\mathrm{2}} }{\mathrm{2}} \\ $$ Answered by witcher3 last updated on 08/Sep/23…
Question Number 196934 by Amidip last updated on 03/Sep/23 Answered by aleks041103 last updated on 04/Sep/23 $${M}\left({x},{y}\right){dx}+{N}\left({x},{y}\right){dy}=\mathrm{0} \\ $$$${if}\:\:\partial_{{y}} {M}=\partial_{{x}} {N},\:{then}\:\exists{F}\left({x},{y}\right): \\ $$$${M}\left({x},{y}\right){dx}+{N}\left({x},{y}\right){dy}={dF}=\mathrm{0}\Rightarrow{F}={const}. \\ $$$${in}\:{our}\:{case}\:\partial_{{y}}…
Question Number 196458 by peter frank last updated on 25/Aug/23 Answered by Peace last updated on 25/Aug/23 $$\int\left({sin}\left({y}\right)+{ycos}\left({y}\right)\right){dh}=\int{x}\left(\mathrm{2}{ln}\left(\mathrm{x}\right)+\mathrm{1}\right)\mathrm{dx} \\ $$$$\Leftrightarrow+{ysin}\left({y}\right)+{c}={x}^{\mathrm{2}} {ln}\left({x}\right) \\ $$$${x}^{\mathrm{2}} {ln}\left({x}\right)−{ysin}\left({y}\right)+{c}=\mathrm{0} \\…
Question Number 196199 by Frix last updated on 19/Aug/23 $$\mathrm{Solve}: \\ $$$${y}'''=\frac{\mathrm{3}{y}'\left({y}''\right)^{\mathrm{2}} }{\mathrm{1}+\left({y}'\right)^{\mathrm{2}} } \\ $$ Answered by aleks041103 last updated on 20/Aug/23 $$\left({ln}\left({y}''\right)\right)'=\frac{{y}'''}{{y}''}=\frac{\mathrm{3}{y}'{y}''}{\mathrm{1}+\left({y}'\right)^{\mathrm{2}} }=\frac{\mathrm{3}}{\mathrm{2}}\:\frac{\left(\left({y}'\right)^{\mathrm{2}}…