Category: Differential Equation

Question Number 119002 by benjo_mathlover last updated on 21/Oct/20 $$\frac{dy}{dx}=\frac{xy}{x^2+1}andy\left(\sqrt{15}\right)=2$$ Answered by bramlexs22 last updated on 21/Oct/20 $$\frac{dy}{y}=\frac{xdx}{x^2+1}\Rightarrow \int \frac{dy}{y}=\int \frac{xdx}{x^2+1}$$$$\mathrm{ln}\:\left({y}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\left({x}^{\mathrm{2}}…

Question Number 118962 by benjo_mathlover last updated on 21/Oct/20 $$xdy=(y+\sqrt{x^2+y^2})dx;y\left(\sqrt{3}\right)=1$$ Answered by TANMAY PANACEA last updated on 21/Oct/20 $$\frac{{xdy}−{ydx}}{{x}^{\mathrm{2}} }=\frac{\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}}…

Question Number 118917 by htet last updated on 20/Oct/20 $$x(x+y)dy-x^{2}dx$$ Commented by Dwaipayan Shikari last updated on 20/Oct/20 $$Q118588$$ Terms…

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

Question Number 118442 by bramlexs22 last updated on 17/Oct/20 $$\sin x.y^{″}+2\cos x.y^{\prime }-y\sin x=e^x$$$$$$ Answered by john santu last updated on 17/Oct/20 $$Tosolveit,wewriteitfirstas$$$$\left(\mathrm{sin}\:{x}.{y}''+\mathrm{cos}\:{x}.{y}'\:\right)+\:\left(\mathrm{cos}\:{x}.{y}'\:−\mathrm{sin}\:{x}\right)=\:{e}^{{x}}…