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Category: Differential Equation

y-1-2x-7-3-

Question Number 68327 by 9102176137086 last updated on 08/Sep/19 $${y}=\left(\mathrm{1}−\mathrm{2}{x}^{−\mathrm{7}} \right)^{\mathrm{3}} \\ $$ Answered by $@ty@m123 last updated on 09/Sep/19 $${Please}\:{do}\:{not}\:{spoil}\:{the}\:{flow}\:{of}\:{this}\:{forum} \\ $$$${with}\:{a}\:{flood}\:{of}\:{similar}\:{questions}. \\ $$$${See}\:{solved}\:{examples}\:{in}\:{your}…

d-2-y-dx-2-sin-3x-e-x-x-2-when-y-0-1-and-y-0-0-Find-the-solution-

Question Number 133776 by bramlexs22 last updated on 24/Feb/21 $$\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:=\:\mathrm{sin}\:\mathrm{3x}\:+\:\mathrm{e}^{\mathrm{x}} \:+\:\mathrm{x}^{\mathrm{2}} \:,\:\mathrm{when}\:\mathrm{y}'\left(\mathrm{0}\right)=\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{y}\left(\mathrm{0}\right)=\:\mathrm{0}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{solution} \\ $$ Answered by bobhans last updated on 24/Feb/21…

y-bx-ay-ax-by-

Question Number 133631 by liberty last updated on 23/Feb/21 $$\mathrm{y}'\:=\:\frac{\mathrm{bx}+\mathrm{ay}}{\mathrm{ax}+\mathrm{by}} \\ $$ Answered by TheSupreme last updated on 23/Feb/21 $${caso}\:\mathrm{1}:\:{b}=\mathrm{0}\: \\ $$$${y}'=\frac{{ay}}{{ax}}=\frac{{y}}{{x}} \\ $$$${ln}\left({y}\right)={ln}\left({x}\right)+{c} \\…

Question-67991

Question Number 67991 by ramirez105 last updated on 03/Sep/19 Commented by mathmax by abdo last updated on 03/Sep/19 $${xy}\:{dx}+\mathrm{2}\left({x}^{\mathrm{2}} \:+\mathrm{2}{y}^{\mathrm{2}} \right){dy}\:=\mathrm{0}\:\Rightarrow\mathrm{2}\left({x}^{\mathrm{2}} \:+\mathrm{2}{y}^{\mathrm{2}} \right){dy}\:=−{xydx}\:\Rightarrow \\ $$$$\mathrm{2}\frac{{dy}}{{y}}\:=\frac{−{xdx}}{{x}^{\mathrm{2}}…