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Category: Differential Equation

sin-x-y-2cos-x-y-y-sin-x-e-x-

Question Number 118442 by bramlexs22 last updated on 17/Oct/20 $$\:\:\mathrm{sin}\:{x}.{y}''\:+\mathrm{2cos}\:{x}.\:{y}'−{y}\:\mathrm{sin}\:{x}\:=\:{e}^{{x}} \\ $$$$ \\ $$ Answered by john santu last updated on 17/Oct/20 $$\:{To}\:{solve}\:{it},\:{we}\:{write}\:{it}\:{first}\:{as}\: \\ $$$$\left(\mathrm{sin}\:{x}.{y}''+\mathrm{cos}\:{x}.{y}'\:\right)+\:\left(\mathrm{cos}\:{x}.{y}'\:−\mathrm{sin}\:{x}\right)=\:{e}^{{x}}…

If-a-curve-y-f-x-passing-through-the-point-1-2-is-the-solution-of-differential-equation-2x-2-dy-2xy-y-2-dx-then-the-value-of-f-2-is-equal-to-

Question Number 118376 by bramlexs22 last updated on 17/Oct/20 $${If}\:{a}\:{curve}\:{y}\:=\:{f}\left({x}\right)\:{passing}\:{through} \\ $$$${the}\:{point}\:\left(\mathrm{1},\mathrm{2}\right)\:{is}\:{the}\:{solution} \\ $$$${of}\:{differential}\:{equation} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} \:{dy}\:=\:\left(\mathrm{2}{xy}+{y}^{\mathrm{2}} \right){dx}\:,\:{then}\:{the}\: \\ $$$${value}\:{of}\:{f}\left(\mathrm{2}\right)\:{is}\:{equal}\:{to}? \\ $$ Answered by benjo_mathlover…

y-3y-2y-1-1-e-x-

Question Number 118274 by bobhans last updated on 16/Oct/20 $$\:\:{y}''−\mathrm{3}{y}'+\mathrm{2}{y}\:=\:\frac{\mathrm{1}}{\mathrm{1}+{e}^{−{x}} }\: \\ $$ Answered by mathmax by abdo last updated on 16/Oct/20 $$\mathrm{h}\rightarrow\mathrm{r}^{\mathrm{2}} −\mathrm{3r}+\mathrm{2}=\mathrm{0}\:\rightarrow\Delta=\mathrm{9}−\mathrm{8}=\mathrm{1}\:\Rightarrow\mathrm{r}_{\mathrm{1}} =\frac{\mathrm{3}+\mathrm{1}}{\mathrm{2}}=\mathrm{2}\:\mathrm{and}\:\mathrm{r}_{\mathrm{2}}…

Question-183533

Question Number 183533 by MikeH last updated on 26/Dec/22 Commented by MikeH last updated on 26/Dec/22 $$\mathrm{please}\:\mathrm{guys}\:\mathrm{solve}\:\mathrm{using}\:\mathrm{the}\:\mathrm{method}\:\mathrm{undetermined} \\ $$$$\mathrm{coefficients}\:\mathrm{or}\:\mathrm{variation}\:\mathrm{of}\:\mathrm{parameters}. \\ $$ Answered by qaz last…

Question-183532

Question Number 183532 by MikeH last updated on 26/Dec/22 Answered by CElcedricjunior last updated on 26/Dec/22 $$\mathrm{3}\boldsymbol{{xy}}'−\boldsymbol{{y}}=\boldsymbol{{lnx}}+\mathrm{1}\:\:\:\:\boldsymbol{{y}}\left(\mathrm{1}\right)=−\mathrm{2} \\ $$$$\left(\boldsymbol{{h}}\right):\mathrm{3}\boldsymbol{{xy}}'−\boldsymbol{{y}}=\mathrm{0}=>\boldsymbol{{y}}=\boldsymbol{{e}}^{\int\frac{\mathrm{1}}{\mathrm{3}\boldsymbol{{x}}}\boldsymbol{{dx}}} =\boldsymbol{{ke}}^{\frac{\mathrm{1}}{\mathrm{3}}\boldsymbol{{ln}}\mid\boldsymbol{{x}}\mid} =\boldsymbol{{ke}}^{\frac{\mathrm{1}}{\mathrm{3}}\boldsymbol{{lnx}}} \boldsymbol{{pour}}\:\boldsymbol{{x}}\in\mathbb{R}_{+} ^{\ast} \\ $$$$\boldsymbol{{y}}=\boldsymbol{{k}}\sqrt[{\mathrm{3}}]{\boldsymbol{{x}}}…