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Category: Differential Equation

2×2-9x-10-

Question Number 16918 by rustylee last updated on 28/Jun/17 $$\mathrm{2}{x}\mathrm{2}+\mathrm{9}{x}=\mathrm{10} \\ $$ Answered by Joel577 last updated on 28/Jun/17 $$\mathrm{2}{x}^{\mathrm{2}} \:+\:\mathrm{9}{x}\:−\:\mathrm{10}\:=\:\mathrm{0} \\ $$$${x}_{\mathrm{1},\mathrm{2}} \:=\:\frac{−\mathrm{9}\:\pm\:\sqrt{\mathrm{81}\:+\:\mathrm{80}}}{\mathrm{4}} \\…

how-to-minimalize-t-x-2-x-1-1-y-x-2-x-2-y-x-2-c-1-c-0-x-t-

Question Number 147762 by DomaPeti last updated on 23/Jul/21 $${how}\:{to}\:{minimalize}\:{t}? \\ $$$$\underset{{x}_{\mathrm{2}} } {\overset{{x}_{\mathrm{1}} } {\int}}\frac{\sqrt{\mathrm{1}+\left({y}\left({x}\right)'\right)^{\mathrm{2}} }}{\:\sqrt{{x}^{\mathrm{2}} +{y}\left({x}\right)^{\mathrm{2}} }\centerdot{c}_{\mathrm{1}} +{c}_{\mathrm{0}} }\Delta{x}={t} \\ $$$$ \\ $$…

dv-dt-kv-bt-where-k-and-b-are-constants-solve-the-equation-of-v-given-v-u-when-t-0-

Question Number 16546 by Sai dadon. last updated on 23/Jun/17 $${dv}/{dt}=−\left({kv}+{bt}\right)\:{where}\:{k}\:{and}\:{b}\:{are}\:{constants} \\ $$$${solve}\:{the}\:{equation}\:{of}\:{v}\:{given} \\ $$$${v}={u}\:{when}\:{t}=\mathrm{0} \\ $$ Answered by mrW1 last updated on 23/Jun/17 $$\frac{\mathrm{dv}}{\mathrm{dt}}+\mathrm{kv}=−\mathrm{bt}…

Help-plz-Given-2d-2-x-dt-2-2dx-dt-x-ksint-where-k-is-constant-show-that-if-x-n-and-dx-dt-0-when-t-0-then-x-e-1-2t-n-2-5k-cos-t-2-n-4-5k-sin-t-2-1-5ksint-2-5kcost-

Question Number 16514 by Sai dadon. last updated on 23/Jun/17 $${Help}\:{plz} \\ $$$${Given}\:\mathrm{2}{d}^{\mathrm{2}} {x}/{dt}^{\mathrm{2}} +\mathrm{2}{dx}/{dt}+{x}={ksint} \\ $$$${where}\:{k}\:{is}\:{constant}\:{show}\:{that}\:{if}\:{x}={n} \\ $$$${and}\:{dx}/{dt}=\mathrm{0}\:{when}\:{t}=\mathrm{0}\:{then}\: \\ $$$$\left.{x}={e}^{−\mathrm{1}/\mathrm{2}{t}} \left\{\left({n}+\mathrm{2}/\mathrm{5}{k}\right){cos}\left({t}/\mathrm{2}\right)+\right)+\left({n}+\mathrm{4}/\mathrm{5}{k}\right){sin}\left({t}/\mathrm{2}\right)\right\} \\ $$$$−\mathrm{1}/\mathrm{5}{ksint}−\mathrm{2}/\mathrm{5}{kcost}. \\…