Category: Differential Equation

Question Number 191960 by Rupesh123 last updated on 04/May/23 Answered by a.lgnaoui last updated on 05/May/23 $$\mathbf{f}(\mathbf{f}\left(\mathbf{x}\right)-\mathbf{f}\left(\mathbf{y}\right))=\mathbf{f}(\mathbf{f}\left(\mathbf{x}\right)-2{\mathbf{x}}^2\mathbf{f}\left(\mathbf{y}\right)+\mathbf{f}\left({\mathbf{y}}^2\right)$$$$\:\:\Rightarrow\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)−\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{y}}\right)\right)=\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)\right)−\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{y}}\right)+\boldsymbol{\mathrm{f}}^{−\mathrm{1}}…

Question Number 126285 by bramlexs22 last updated on 19/Dec/20 $$\Rightarrow solve{x}^{2}y={\int }_1^{x^2}f\left(\sqrt{t}\right)dx+x^3+\frac{1}{x}+1$$$$y=f\left(x\right)=?$$ Answered by liberty last updated on…

Question Number 126229 by MathSh last updated on 18/Dec/20 $$(1+y)x^{\prime }=x$$ Answered by Dwaipayan Shikari last updated on 18/Dec/20 $$(1+y)\frac{dx}{dy}=x\Rightarrow \int \frac{dy}{1+y}=\int \frac{dx}{x}\Rightarrow 1+y=Cx$$ Answered by…

Question Number 126223 by liberty last updated on 18/Dec/20 $$\frac{dy}{dx}+\frac{x^{2}y}{x^3+y^3}=0$$ Commented by bramlexs22 last updated on 18/Dec/20 $$\:{v}+{x}\frac{{dv}}{{dx}}\:=\:\frac{{x}^{\mathrm{3}} {v}}{{x}^{\mathrm{3}} \left(\mathrm{1}+{v}^{\mathrm{3}}…

Question Number 126122 by benjo_mathlover last updated on 17/Dec/20 $$y.y^{\prime }+3y=2x$$ Answered by Dwaipayan Shikari last updated on 17/Dec/20 $$y^{\prime }+3=\frac{2x}{y}y=vx\Rightarrow y^{\prime }=v+{xv}^{\prime }$$$$\Rightarrow{xv}'+{v}+\mathrm{3}=\frac{\mathrm{2}}{{v}}\Rightarrow{xv}'=\frac{\mathrm{2}−{v}^{\mathrm{2}} −\mathrm{3}{v}}{{v}} \…