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Category: Differential Equation

Solve-y-3y-y-2-1-y-2-

Question Number 196199 by Frix last updated on 19/Aug/23 $$\mathrm{Solve}: \\ $$$${y}'''=\frac{\mathrm{3}{y}'\left({y}''\right)^{\mathrm{2}} }{\mathrm{1}+\left({y}'\right)^{\mathrm{2}} } \\ $$ Answered by aleks041103 last updated on 20/Aug/23 $$\left({ln}\left({y}''\right)\right)'=\frac{{y}'''}{{y}''}=\frac{\mathrm{3}{y}'{y}''}{\mathrm{1}+\left({y}'\right)^{\mathrm{2}} }=\frac{\mathrm{3}}{\mathrm{2}}\:\frac{\left(\left({y}'\right)^{\mathrm{2}}…

x-2-y-11-x-y-2-7-x-y-

Question Number 195301 by SajaRashki last updated on 29/Jul/23 $$\begin{cases}{{x}^{\mathrm{2}} +{y}=\mathrm{11}}\\{{x}+{y}^{\mathrm{2}} =\mathrm{7}}\end{cases}\Rightarrow\:{x},{y}=? \\ $$ Answered by AST last updated on 30/Jul/23 $${y}=\mathrm{11}−{x}^{\mathrm{2}} \Rightarrow\left(\mathrm{11}−{x}^{\mathrm{2}} \right)^{\mathrm{2}} =\mathrm{7}−{x}…\left({i}\right)…

A-tank-contains-300-litres-of-fluid-in-which-20-grams-of-salt-is-dissolved-Brine-containing-1-gm-of-salt-per-litre-is-then-pumped-into-the-tank-at-a-rate-of-4L-min-the-well-mixed-solution-is-p

Question Number 194599 by pete last updated on 10/Jul/23 $$\mathrm{A}\:\mathrm{tank}\:\mathrm{contains}\:\mathrm{300}\:\mathrm{litres}\:\mathrm{of}\:\mathrm{fluid}\:\mathrm{in}\: \\ $$$$\mathrm{which}\:\mathrm{20}\:\mathrm{grams}\:\mathrm{of}\:\mathrm{salt}\:\mathrm{is}\:\mathrm{dissolved}.\: \\ $$$$\mathrm{Brine}\:\mathrm{containing}\:\:\mathrm{1}\:\mathrm{gm}\:\mathrm{of}\:\mathrm{salt}\:\mathrm{per}\:\mathrm{litre} \\ $$$$\:\mathrm{is}\:\mathrm{then}\:\mathrm{pumped}\:\mathrm{into}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{at}\:\mathrm{a}\:\mathrm{rate} \\ $$$$\:\mathrm{of}\:\mathrm{4L}/\mathrm{min};\:\mathrm{the}\:\mathrm{well}\:\mathrm{mixed}\:\mathrm{solution}\: \\ $$$$\mathrm{is}\:\mathrm{pumped}\:\mathrm{out}\:\mathrm{at}\:\mathrm{the}\:\mathrm{same}\:\mathrm{rate}. \\ $$$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{N}\left(\mathrm{t}\right)\:\mathrm{of}\:\mathrm{grams}\:\mathrm{of} \\ $$$$\:\mathrm{salt}\:\mathrm{in}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{at}\:\mathrm{time}\:\mathrm{t}.\: \\…

Find-the-ordinary-differential-equation-satisfy-by-y-x-n-A-Blogx-

Question Number 193733 by Tawa11 last updated on 18/Jun/23 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{ordinary}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\mathrm{satisfy}\:\mathrm{by}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\:\:=\:\:\mathrm{x}^{\mathrm{n}} \left(\mathrm{A}\:\:+\:\:\mathrm{Blogx}\right) \\ $$ Answered by Rajpurohith last updated on 19/Jun/23 $${y}\:'={x}^{{n}}…