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Category: Differential Equation

solve-the-Cauchy-Euler-Differential-Equation-by-substituting-x-e-t-x-3-d-3-y-dx-3-2x-2-d-2-y-dx-2-2y-10x-10-x-

Question Number 116105 by ShakaLaka last updated on 30/Sep/20 $${solve}\:{the}\:{Cauchy}-{Euler}\: \\ $$$${Differential}\:{Equation}\:{by} \\ $$$${substituting}\:{x}={e}^{{t}} \\ $$$${x}^{\mathrm{3}} \:\frac{{d}^{\mathrm{3}} {y}}{{dx}^{\mathrm{3}} }\:+\:\mathrm{2}{x}^{\mathrm{2}} \:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{2}{y}\:=\:\mathrm{10}{x}\:+\:\frac{\mathrm{10}}{{x}} \\ $$$$ \\…

y-dy-dx-1-x-2-y-

Question Number 116053 by Study last updated on 30/Sep/20 $${y}\frac{{dy}}{{dx}}=\mathrm{1}+{x}^{\mathrm{2}} \:\:\:\:\:\:\:\:{y}=? \\ $$ Answered by Dwaipayan Shikari last updated on 30/Sep/20 $$\mathrm{y}\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{1}+\mathrm{x}^{\mathrm{2}} \\ $$$$\int\mathrm{ydy}=\int\mathrm{1}+\mathrm{x}^{\mathrm{2}} \mathrm{dx}…

Question-115968

Question Number 115968 by Engr_Jidda last updated on 29/Sep/20 Answered by 1549442205PVT last updated on 30/Sep/20 $$\mathrm{Put}\:\mathrm{u}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{1};\mathrm{v}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{y}^{\mathrm{2}} +\mathrm{1} \\ $$$$\mathrm{The}\:\mathrm{condition}\:\mathrm{Cauchy}−\mathrm{Rieman}\:\mathrm{for} \\ $$$$\mathrm{the}\:\mathrm{analytical}\:\mathrm{is}\:\frac{\partial\mathrm{u}}{\partial\mathrm{x}}=\frac{\partial\mathrm{v}}{\partial\mathrm{y}}\left(\mathrm{1}\right),\frac{\partial\mathrm{u}}{\partial\mathrm{y}}=−\frac{\partial\mathrm{v}}{\partial\mathrm{x}}\left(\mathrm{2}\right) \\ $$$$\mathrm{We}\:\mathrm{have}\:\frac{\partial\mathrm{u}}{\partial\mathrm{x}}=\mathrm{2x},\frac{\partial\mathrm{u}}{\partial\mathrm{y}}=\mathrm{0},\frac{\partial\mathrm{v}}{\partial\mathrm{x}}=\mathrm{0},\frac{\partial\mathrm{v}}{\partial\mathrm{y}}=\mathrm{2y}…