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Category: Differential Equation

please-check-my-answer-x-2y-5-dx-2x-y-4-dy-0-X-x-a-amp-Y-y-b-X-a-2Y-2b-5-dX-2X-2a-Y-b-4-dY-0-a-2b-5-2a-b-4-a-1-b-2-X-2Y-dX-2X-Y-dY-0-Y-XV-dY-dX-V-X-dV-dx-X-2XV-2X-XV-V-X

Question Number 197389 by uchihayahia last updated on 16/Sep/23 $$ \\ $$$${please}\:{check}\:{my}\:{answer} \\ $$$$\:\left({x}−\mathrm{2}{y}+\mathrm{5}\right){dx}+\left(\mathrm{2}{x}−{y}+\mathrm{4}\right){dy}=\mathrm{0} \\ $$$$\:{X}={x}+{a}\:\&\:{Y}={y}+{b} \\ $$$$ \\ $$$$\:\left({X}−{a}−\mathrm{2}{Y}+\mathrm{2}{b}+\mathrm{5}\right){dX}+\left(\mathrm{2}{X}−\mathrm{2}{a}−{Y}+{b}+\mathrm{4}\right){dY}=\mathrm{0} \\ $$$$\:-{a}+\mathrm{2}{b}=-\mathrm{5} \\ $$$$\:-\mathrm{2}{a}+{b}=-\mathrm{4} \\…

Question-196934

Question Number 196934 by Amidip last updated on 03/Sep/23 Answered by aleks041103 last updated on 04/Sep/23 $${M}\left({x},{y}\right){dx}+{N}\left({x},{y}\right){dy}=\mathrm{0} \\ $$$${if}\:\:\partial_{{y}} {M}=\partial_{{x}} {N},\:{then}\:\exists{F}\left({x},{y}\right): \\ $$$${M}\left({x},{y}\right){dx}+{N}\left({x},{y}\right){dy}={dF}=\mathrm{0}\Rightarrow{F}={const}. \\ $$$${in}\:{our}\:{case}\:\partial_{{y}}…

Question-196458

Question Number 196458 by peter frank last updated on 25/Aug/23 Answered by Peace last updated on 25/Aug/23 $$\int\left({sin}\left({y}\right)+{ycos}\left({y}\right)\right){dh}=\int{x}\left(\mathrm{2}{ln}\left(\mathrm{x}\right)+\mathrm{1}\right)\mathrm{dx} \\ $$$$\Leftrightarrow+{ysin}\left({y}\right)+{c}={x}^{\mathrm{2}} {ln}\left({x}\right) \\ $$$${x}^{\mathrm{2}} {ln}\left({x}\right)−{ysin}\left({y}\right)+{c}=\mathrm{0} \\…

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)…