Question Number 1211 by 112358 last updated on 14/Jul/15 $${Is}\:{there}\:{a}\:{solution}\:{of}\:{y}\:{in}\:{terms} \\ $$$${of}\:{x}\:{for}\:{the}\:{following}\:{D}.{E}? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{{dy}}{{dx}}+\frac{{c}_{\mathrm{1}} }{{y}\left({c}_{\mathrm{2}} {x}+{c}_{\mathrm{3}} \right)^{\mathrm{2}} }={c}_{\mathrm{4}} \\ $$$${Here}\:{c}_{\mathrm{1}} ,\:{c}_{\mathrm{2}} ,\:{c}_{\mathrm{3}} ,\:{c}_{\mathrm{4}} \:{are}\:{constants}.\: \\…
Question Number 970 by 123456 last updated on 09/May/15 $${m}\frac{{d}\boldsymbol{{v}}}{{dt}}={q}\left(\boldsymbol{{v}}×\boldsymbol{{B}}+\boldsymbol{{E}}\right)+\boldsymbol{{f}} \\ $$$$\boldsymbol{{v}}\left(\mathrm{0}\right)=\boldsymbol{{v}}_{\mathrm{0}} \\ $$$$\boldsymbol{{v}}\left({t}\right)=? \\ $$$$\boldsymbol{{v}}=\frac{{d}\boldsymbol{{r}}}{{dt}} \\ $$$$\boldsymbol{{r}}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\boldsymbol{{r}}\left({t}\right)=?? \\ $$ Terms of Service…
Question Number 776 by 123456 last updated on 12/Mar/15 $$\frac{\partial^{\mathrm{2}} {u}}{\partial{x}^{\mathrm{2}} }={v}_{\mathrm{1}} \frac{\partial^{\mathrm{2}} {u}}{\partial{x}\partial{t}}+{v}_{\mathrm{2}} ^{\mathrm{2}} \frac{\partial^{\mathrm{2}} {u}}{\partial{t}^{\mathrm{2}} } \\ $$$${u}\left({x},\mathrm{0}\right)={f}\left({x}\right) \\ $$$${u}_{{t}} \left({x},\mathrm{0}\right)={g}\left({x}\right) \\ $$…
Question Number 767 by 123456 last updated on 09/Mar/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$$\frac{{d}\left({fg}\right)}{{dx}}=\frac{{df}}{{dx}}\centerdot\frac{{dg}}{{dx}} \\ $$$$\frac{{d}\left({f}^{\mathrm{2}} \right)}{{dx}}=\frac{{df}}{{dx}}\centerdot\frac{{df}}{{dx}} \\ $$$$\frac{{d}\left({g}^{\mathrm{2}} \right)}{{dx}}=? \\ $$ Commented by 123456…
Question Number 757 by 123456 last updated on 07/Mar/15 $${k}\frac{{d}^{\mathrm{2}} {i}}{{dt}^{\mathrm{2}} }+{l}\frac{{di}}{{dt}}+{ri}={v} \\ $$$${i}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${i}'\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${k},{l},{r},{v}\:{are}\:{constants} \\ $$ Commented by prakash jain last…
Question Number 131805 by Engr_Jidda last updated on 08/Feb/21 $${obtain}\:{the}\:{series}\:{solution}\:{of}\:{the}\:{differential}\: \\ $$$${equation}:\:{y}^{{II}} +{xy}^{{I}} −{y}={x}^{\mathrm{2}} +\mathrm{1} \\ $$$${y}\left(\mathrm{0}\right)=\mathrm{1}\:{and}\:{y}^{{I}} \left(\mathrm{0}\right)=\mathrm{2} \\ $$ Answered by physicstutes last updated…
Question Number 730 by 123456 last updated on 04/Mar/15 $$\mathrm{sin}\:{t}={i}\frac{{di}}{{dt}} \\ $$$${i}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${i}\left({t}\right)=? \\ $$ Commented by malwaan last updated on 05/Mar/15 $$−{cos}\:{t}=\frac{{i}^{\mathrm{2}} }{\mathrm{2}}+{C}\:…
Question Number 131644 by Ahmed1hamouda last updated on 07/Feb/21 Commented by Ahmed1hamouda last updated on 07/Feb/21 $$ \\ $$$$\mathrm{solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$ Answered by rs4089 last…
Question Number 519 by Yugi last updated on 25/Jan/15 $${Find}\:{the}\:{sum}\:\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\left(\mathrm{3}{r}+\mathrm{5}\right)\begin{pmatrix}{{n}}\\{{r}}\end{pmatrix}=\mathrm{5}\begin{pmatrix}{{n}}\\{\mathrm{0}}\end{pmatrix}\:+\mathrm{8}\begin{pmatrix}{{n}}\\{\mathrm{1}}\end{pmatrix}\:+\mathrm{11}\begin{pmatrix}{{n}}\\{\mathrm{2}}\end{pmatrix}\:+…\left(\mathrm{3}{n}+\mathrm{5}\right)\begin{pmatrix}{{n}}\\{{n}}\end{pmatrix}\: \\ $$$${as}\:{a}\:{simple}\:{function}\:{of}\:{n}. \\ $$ Commented by prakash jain last updated on 22/Jan/15 $$\underset{{r}=\mathrm{0}}…
Question Number 517 by Yugi last updated on 25/Jan/15 $${A}\:{person}\:{is}\:{said}\:{to}\:{be}\:{n}\:{years}\:{old}\:\left(\:{where}\:{n}\:{is}\:{a}\:{non}−{negative}\:{integer}\right)\:{if}\: \\ $$$${the}\:{person}\:{has}\:{lived}\:{at}\:{least}\:{n}\:{years}\:{and}\:{has}\:{not}\:{lived}\:{n}+\mathrm{1}\:{years}.\:{At}\:{some}\:{point} \\ $$$${Tom}\:{is}\:\mathrm{4}\:{years}\:{old}\:{and}\:{John}\:{is}\:{three}\:{times}\:{as}\:{old}\:{as}\:{Mary}.\:{At}\:{another}\:{time}, \\ $$$${Mary}\:{is}\:{twice}\:{as}\:{old}\:{as}\:{Tom}\:{and}\:{John}\:{is}\:{five}\:{times}\:{as}\:{old}\:{as}\:{Tom}.\:{At}\:{a}\:{third}\: \\ $$$${time},\:{John}\:{is}\:{twice}\:{as}\:{old}\:{as}\:{Mary}\:{and}\:{Tom}\:{is}\:{t}\:{years}\:{old}.\:{What}\:{is}\:{the}\:{largest} \\ $$$${possible}\:{value}\:{of}\:{t}? \\ $$ Commented by prakash…