Category: Differential Equation

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 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 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 131551 by liberty last updated on 06/Feb/21 $$\mathrm{Use}\:\mathrm{Euler}\:\mathrm{method}\:\mathrm{to}\:\mathrm{estimate}\: \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{solution}\:\mathrm{at}\:\mathrm{given}\: \\ $$$$\mathrm{point}\:\mathrm{x}^{\ast} \:.\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{5xe}^{\mathrm{x}^{\mathrm{5}} } \:,\mathrm{y}\left(\mathrm{0}\right)=\mathrm{1}\:,\mathrm{dx}=\mathrm{0}.\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{x}^{\ast} =\mathrm{1}. \\ $$ Terms of Service…