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Category: Differential Equation

Question-191960

Question Number 191960 by Rupesh123 last updated on 04/May/23 Answered by a.lgnaoui last updated on 05/May/23 $$\:\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)−\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{y}}\right)\right)=\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)−\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{y}}\right)+\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{y}}^{\mathrm{2}} \right)\right. \\ $$$$\:\:\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-126408

Question Number 126408 by morarupaula last updated on 20/Dec/20 Answered by Dwaipayan Shikari last updated on 20/Dec/20 $$\overset{\bullet\bullet\bullet} {{x}}+\overset{\bullet} {{x}}=\mathrm{0}\:\:\:\:\:\:\:{x}={e}^{\lambda{t}} \\ $$$$\lambda^{\mathrm{3}} +\lambda=\mathrm{0}\Rightarrow\lambda=\mathrm{0}\:,\:\lambda=\pm{i} \\ $$$${x}=\Lambda+\Gamma{e}^{\lambda{ti}}…

1-y-x-x-

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