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Category: Differential Equation

Question-68855

Question Number 68855 by ramirez105 last updated on 16/Sep/19 Commented by kaivan.ahmadi last updated on 16/Sep/19 $${set}\:{M}=\mathrm{6}{x}+{y}^{\mathrm{2}} \:\:{and}\:{N}={y}\left(\mathrm{2}{x}−\mathrm{3}{y}\right) \\ $$$$\frac{\partial{M}}{\partial{y}}=\mathrm{2}{y}\:=\frac{\partial{N}}{\partial{x}}\Rightarrow{the}\:{equation}\:{is}\:{exact} \\ $$$$\frac{\partial{u}}{\partial{x}}=\mathrm{6}{x}+{y}^{\mathrm{2}} \:\:\:{and}\:\:\frac{\partial{u}}{\partial{y}}={y}\left(\mathrm{2}{x}−\mathrm{3}{y}\right)=\mathrm{2}{xy}−\mathrm{3}{y}^{\mathrm{2}} \\ $$$$\Rightarrow{u}\left({x},{y}\right)=\int\left(\mathrm{6}{x}+{y}^{\mathrm{2}}…

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…