Question Number 61635 by ajfour last updated on 05/Jun/19 $$\mathrm{2}\left(\int_{\mathrm{0}} ^{\:{x}} {y}^{\mathrm{3}} \mathrm{cos}\:{xdx}\right)\left[\frac{{yd}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }−\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} \right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\:{ky}^{\mathrm{5}} \mathrm{sin}\:{x}\:\:\:\:\:;\:\: \\ $$$$\:\:{y}\left(\mathrm{0}\right)={a},\:{y}'\left(\mathrm{0}\right)=\mathrm{0}\:. \\ $$$$\:{solve}\:{the}\:{differential}\:{equation}. \\ $$$$\left({Laplace}\:{tranforms}\:{might}\right.…
Question Number 127064 by benjo_mathlover last updated on 26/Dec/20 $$\:\:\:\left({D}^{\mathrm{2}} −\mathrm{1}\right){y}\:=\:{x}\:\mathrm{sin}\:{x}\: \\ $$ Answered by liberty last updated on 26/Dec/20 $$\:{The}\:{characteristic}\:{eq}\:{of}\:\left({D}^{\mathrm{2}} −\mathrm{1}\right){y}\:=\:\mathrm{0} \\ $$$${is}\:\lambda^{\mathrm{2}} −\mathrm{1}=\mathrm{0}\:,\:{has}\:{the}\:{roots}\:\lambda=\pm\mathrm{1}…
Question Number 126960 by bramlexs22 last updated on 25/Dec/20 $$\:{using}\:{Frobenius}\:{method} \\ $$$${x}^{\mathrm{2}} {y}''\:+\mathrm{6}{xy}'\:+\left(\mathrm{4}{x}^{\mathrm{2}} +\mathrm{6}\right){y}\:=\:\mathrm{0} \\ $$ Commented by liberty last updated on 26/Dec/20 $${put}\:{y}={e}^{{rx}} \:\rightarrow\begin{cases}{{y}'={re}^{{rx}}…
Question Number 126896 by BHOOPENDRA last updated on 25/Dec/20 $${yy}''−\left({y}'\right)^{\mathrm{2}} ={e}^{{ax}\:} {find}\:{genral}\:{solution}? \\ $$ Commented by liberty last updated on 25/Dec/20 $${ok}\:{i}\:{try}\:{solve}\:{it}. \\ $$$$ \\…
Question Number 192345 by Mingma last updated on 15/May/23 Answered by aleks041103 last updated on 15/May/23 $$\int_{\mathrm{0}} ^{\:\mathrm{1}} \left({f}\left(\mathrm{1}+{x}\right)+{f}\left(\mathrm{1}−{x}\right)\right){dx}= \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left(\mathrm{1}+{x}\right){dx}\:−\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {f}\left(\mathrm{1}−{x}\right){d}\left(−{x}\right)=…
Question Number 126791 by BHOOPENDRA last updated on 24/Dec/20 $${yy}''−\left({y}'\right)^{\mathrm{2}} ={e}^{{ax}\:} \:{find}\:{genral}\:{solution}? \\ $$ Commented by BHOOPENDRA last updated on 24/Dec/20 $${help}\:{me}\:{out}\:{this}? \\ $$ Answered…
Question Number 126683 by bramlexs22 last updated on 23/Dec/20 $$\:{solve}\:\left({D}^{\mathrm{2}} +{a}\right){y}\:=\:\mathrm{tan}\:{ax}\: \\ $$ Answered by liberty last updated on 23/Dec/20 $$\left(\mathrm{1}\right)\:{Homogenous}\:{solution} \\ $$$$\:{y}_{{h}} =\:{A}\:\mathrm{cos}\:{ax}\:+\:{B}\:\mathrm{sin}\:{ax}\: \\…
Question Number 61107 by arcana last updated on 29/May/19 $${solve}\:{Cauchy}'{s}\:{problem} \\ $$$${x}'=\:{t}\:+\:\frac{\left(\mu{x}\right)^{\mathrm{2}} }{\mathrm{1}+\left(\mu{x}\right)^{\mathrm{2}} },\:\mu\in\mathbb{R} \\ $$$${x}\left(\mathrm{0}\right)=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 126620 by fajri last updated on 22/Dec/20 $$\frac{{d}^{\mathrm{2}} {y}}{{dx}}\:−\:\mathrm{3}\:\frac{{dy}}{{dx}}\:+\:\mathrm{2}{y}\:=\:{e}^{\mathrm{4}{t}} \:,\:{y}\left(\mathrm{0}\right)\:=\:\mathrm{1},\:{y}'\left(\mathrm{0}\right)\:=\:\mathrm{0} \\ $$$${solve}\:{with}\:{Laplace}\:{Transform}! \\ $$ Answered by Olaf last updated on 22/Dec/20 $$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}}…
Question Number 126543 by pticantor last updated on 21/Dec/20 $$\:\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\underset{{i}=\mathrm{1}} {\overset{{k}} {\prod}}{i}^{{k}} =??? \\ $$ Answered by MJS_new last updated on 21/Dec/20 $$=\underset{{k}=\mathrm{1}}…