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Category: Differential Equation

solve-6x-2-3y-2-dx-2xy-dy-

Question Number 118954 by bramlexs22 last updated on 21/Oct/20 $${solve}\:\left(\mathrm{6}{x}^{\mathrm{2}} \:+\:\mathrm{3}{y}^{\mathrm{2}} \right)\:{dx}\:=\:\mathrm{2}{xy}\:{dy} \\ $$ Answered by john santu last updated on 21/Oct/20 $$\:{set}\:{y}\:=\:{gx}\:\Rightarrow\frac{{dy}}{{dx}}\:=\:{g}\:+\:{x}\:\frac{{dg}}{{dx}} \\ $$$${the}\:{differential}\:{equation}\:{can}\:{be}\:{we}…

x-x-y-dy-x-2-dx-0-

Question Number 118588 by bramlexs22 last updated on 18/Oct/20 $${x}\left({x}+{y}\right)\:{dy}\:−{x}^{\mathrm{2}} \:{dx}\:=\:\mathrm{0}\: \\ $$ Commented by Dwaipayan Shikari last updated on 18/Oct/20 $${x}\left({x}+{y}\right)\frac{{dy}}{{dx}}−{x}^{\mathrm{2}} =\mathrm{0} \\ $$$$\frac{{dy}}{{dx}}\left({x}+{y}\right)={x}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…

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}}…