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Category: Differential Equation

1-2x-y-4x-2-y-8y-0-

Question Number 108491 by Ar Brandon last updated on 17/Aug/20 $$\left(\mathrm{1}+\mathrm{2x}\right)\mathrm{y}''+\left(\mathrm{4x}−\mathrm{2}\right)\mathrm{y}'−\mathrm{8y}=\mathrm{0} \\ $$ Answered by Ar Brandon last updated on 20/Aug/20 $$\mathrm{6}.\:\left(\mathrm{1}+\mathrm{2x}\right)\mathrm{y}''+\left(\mathrm{4x}−\mathrm{2}\right)\mathrm{y}'−\mathrm{8y}=\mathrm{0} \\ $$$$\Rightarrow\left(\mathrm{2x}+\mathrm{1}\right)\left(\mathrm{y}''+\mathrm{2y}'\right)+\mathrm{4}\left(\mathrm{y}'+\mathrm{2y}\right)=\mathrm{0} \\…

Show-that-x-3-y-3-1-is-a-solution-to-the-differential-equation-20x-3-3y-2-d-2-y-dx-2-6y-dy-dx-2-0-

Question Number 173733 by Tawa11 last updated on 17/Jul/22 $$\mathrm{Show}\:\mathrm{that}\:\:\:\:\mathrm{x}^{\mathrm{3}} \:\:+\:\:\mathrm{y}^{\mathrm{3}} \:\:=\:\:\mathrm{1}\:\:\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{the}\:\mathrm{differential} \\ $$$$\mathrm{equation}\:\:\:\:\mathrm{20x}^{\mathrm{3}} \:\:\:+\:\:\:\mathrm{3y}^{\mathrm{2}} \:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:\:\:\:+\:\:\:\mathrm{6y}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{\mathrm{2}} \:\:\:=\:\:\:\:\mathrm{0} \\ $$ Commented by kaivan.ahmadi last…

Show-that-x-2-2xy-3y-2-1-is-a-solution-to-the-differential-equation-x-3y-2-d-2-y-dx-2-2-x-2-2xy-2y-3-0-

Question Number 173736 by Tawa11 last updated on 17/Jul/22 $$\mathrm{Show}\:\mathrm{that}\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \:\:\:+\:\:\:\mathrm{2xy}\:\:\:+\:\:\:\mathrm{3y}^{\mathrm{2}} \:\:\:=\:\:\:\mathrm{1},\:\:\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{differential}\:\mathrm{equation}\:\:\:\:\:\left(\mathrm{x}\:\:\:+\:\:\:\mathrm{3y}\right)^{\mathrm{2}} \:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:\:\:\:\:+\:\:\:\mathrm{2}\left(\mathrm{x}^{\mathrm{2}} \:\:\:+\:\:\:\mathrm{2xy}\:\:\:+\:\:\:\mathrm{2y}^{\mathrm{3}} \right)\:\:\:=\:\:\:\mathrm{0} \\ $$ Answered by mindispower last…

Solve-for-u-and-v-in-the-system-of-equations-below-u-e-2x-cos2x-v-e-2x-sin2x-0-u-e-2x-cos2x-v-e-2x-sin2x-xe-2x-sinx-where-u-and-v-are-functions-of-x-

Question Number 108180 by Ar Brandon last updated on 15/Aug/20 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{u}\:\mathrm{and}\:\mathrm{v}\:\mathrm{in}\:\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations}\:\mathrm{below} \\ $$$$\begin{cases}{\mathrm{u}'\left(\mathrm{e}^{−\mathrm{2x}} \mathrm{cos2x}\right)+\mathrm{v}'\left(\mathrm{e}^{−\mathrm{2x}} \mathrm{sin2x}\right)=\mathrm{0}}\\{\mathrm{u}'\left(\mathrm{e}^{−\mathrm{2x}} \mathrm{cos2x}\right)'+\mathrm{v}'\left(\mathrm{e}^{−\mathrm{2x}} \mathrm{sin2x}\right)'=\mathrm{xe}^{−\mathrm{2x}} \mathrm{sinx}}\end{cases} \\ $$$$\mathrm{where}\:\mathrm{u}\:\mathrm{and}\:\mathrm{v}\:\mathrm{are}\:\mathrm{functions}\:\mathrm{of}\:\mathrm{x} \\ $$ Terms of Service…