Question Number 77605 by lémùst last updated on 08/Jan/20 $$\mathrm{how}\:\mathrm{to}\:\mathrm{solve}\:: \\ $$$$\mathrm{y}''+\mathrm{p}\left(\mathrm{x}\right)\mathrm{y}'+\mathrm{q}\left(\mathrm{x}\right)\mathrm{y}=\mathrm{r}\left(\mathrm{x}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143113 by qaz last updated on 10/Jun/21 $$\mathrm{x}^{\mathrm{3}} =\frac{\mathrm{1}}{\mathrm{3}!}\int_{\mathrm{0}} ^{\mathrm{x}} \mathrm{f}\left(\mathrm{x}−\mathrm{t}\right)\mathrm{f}\left(\mathrm{t}\right)\mathrm{dt} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=? \\ $$ Commented by mr W last updated on 10/Jun/21…
Question Number 77574 by jagoll last updated on 08/Jan/20 $${what}\:{is}\:{maximum}\: \\ $$$${value}\:{of}\:{y}=\:\left(\mathrm{3}{x}+\mathrm{4}\right)^{\mathrm{2}} ×\mathrm{sin}\:\left(\mathrm{2}{x}\right) \\ $$ Commented by MJS last updated on 08/Jan/20 $$\mathrm{sin}\:\mathrm{2}{x}\:=−\mathrm{1}\:\Rightarrow\:{x}={n}\pi−\frac{\pi}{\mathrm{4}}=\frac{\mathrm{4}{n}−\mathrm{1}}{\mathrm{4}}\pi \\ $$$$\mathrm{sin}\:\mathrm{2}{x}\:=+\mathrm{1}\:\Rightarrow\:{x}={n}\pi+\frac{\pi}{\mathrm{4}}=\frac{\mathrm{4}{n}+\mathrm{1}}{\mathrm{4}}\pi…
Question Number 143109 by mnjuly1970 last updated on 10/Jun/21 Commented by mnjuly1970 last updated on 10/Jun/21 $$\:\:\:\:\:{prove}\:\:\mathrm{I}_{\mathrm{1}} =−\frac{\pi^{\mathrm{2}} }{\mathrm{192}}\:\:…..? \\ $$ Answered by qaz last…
Question Number 143086 by mnjuly1970 last updated on 09/Jun/21 $$ \\ $$$$\:\:{Evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\Omega:=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{{ln}\left({tan}\left({x}\right)\right).{sin}^{\pi^{{e}} } \left(\mathrm{2}{x}\right)}{\left({sin}^{\pi^{{e}} } \left({x}\right)+{cos}^{\pi^{{e}} } \left({x}\right)\right)^{\mathrm{2}} }{dx} \\ $$$$…
Question Number 77537 by john santu last updated on 07/Jan/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{solution}\: \\ $$$$\mathrm{xy}'+\left(\mathrm{1}+\mathrm{xcot}\:\mathrm{x}\right)\mathrm{y}=\mathrm{x}\:? \\ $$ Answered by mr W last updated on 07/Jan/20 $${y}'+\left(\frac{\mathrm{1}}{{x}}+\frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}}\right){y}=\mathrm{1} \\…
Question Number 77473 by BK last updated on 06/Jan/20 Commented by mr W last updated on 06/Jan/20 $${y}=\frac{{dy}}{{dx}}+\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\frac{{d}^{\mathrm{3}} {y}}{{dy}^{\mathrm{3}} }+… \\ $$$$\frac{{dy}}{{dx}}=\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}}…
Question Number 11921 by carrot last updated on 05/Apr/17 $${given}\:{that}\:{y}={Acos}\mathrm{5}{x}\:+\:{Bsin}\mathrm{5}{x}, \\ $$$${show}\:{that}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{25}{y}=\mathrm{0} \\ $$ Answered by sandy_suhendra last updated on 05/Apr/17 $$\frac{\mathrm{dy}}{\mathrm{dx}}=−\mathrm{5Asin5x}\:+\:\mathrm{5Bcos5x} \\…
Question Number 11887 by Peter last updated on 04/Apr/17 $$\frac{{dy}}{{dt}}\:+\mathrm{3}{t}^{\mathrm{2}} {y}\:=\:{t}^{\mathrm{2}\:} \:\:\:\:,\:{y}\left(\mathrm{0}\right)\:=\:\mathrm{1} \\ $$$${y}\left({t}\right)\:=\:? \\ $$ Answered by ajfour last updated on 04/Apr/17 $${when}\:\:\frac{{dy}}{{dt}}\:+{P}\:{y}\:={Q} \\…
Question Number 142935 by mnjuly1970 last updated on 07/Jun/21 Answered by qaz last updated on 07/Jun/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}}\mathrm{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}^{\mathrm{2}}…