Category: Differential Equation

Question Number 99992 by bemath last updated on 24/Jun/20 $$\mathrm{y}(1+{\mathrm{x}}^3)\mathrm{dy}-{\mathrm{x}}^2\mathrm{dx}=0;\mathrm{y}\left(2\right)=3$$ Answered by john santu last updated on 24/Jun/20 $$\mathrm{y}\:\mathrm{dy}\:=\:\frac{\mathrm{x}^{\mathrm{2}} \:\mathrm{dx}}{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }…

Question Number 165503 by metamorfose last updated on 02/Feb/22 $$y^{\prime }\left(x\right)=\frac{xln\left(y\left(x\right)\right)}{ln\left(x\right)y\left(x\right)},y\left(x\right)=???.$$ Answered by TheSupreme last updated on 02/Feb/22 $$\frac{{yy}^{\prime }}{ln\left(y\right)}=\frac{x}{ln\left(x\right)}$$$$\frac{x}{ln\left(x\right)}=\frac{y\frac{dy}{dx}}{ln\left(y\right)}$$$$\frac{{xdx}}{{ln}\left({x}\right)}=\frac{{ydy}}{{ln}\left({y}\right)} \…

Question Number 34051 by adil last updated on 29/Apr/18 $$2dy/dx+y=0y\left(0\right)=-3$$ Answered by candre last updated on 30/Apr/18 $$2\frac{dy}{dx}+y=0$$$$\frac{dy}{dx}=-\frac{y}{2}$$$$\frac{{dy}}{{y}}=−\frac{{dx}}{\mathrm{2}} \…

Question Number 99123 by Mr.D.N. last updated on 18/Jun/20 Commented by Rasheed.Sindhi last updated on 18/Jun/20 $$Itseemsthat{you}^{\prime }reexperimenting$$$$aboutcolourschemes.Ifyou$$$$allowmetoexpressmypersonal$$$$openionthenIsaythatredtext$$$${on}\:{black}\:{background}\:{is}\:{not}\:{so}\:…

Question Number 99072 by Mr.D.N. last updated on 18/Jun/20 Answered by mr W last updated on 18/Jun/20 $$\int \frac{x^2+2x-1}{2x^2+3x+1}dx$$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{2}}{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{1}}{dx} \…