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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}…