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Category: Differential Equation

Show-that-for-any-arbitary-constants-A-and-B-y-A-sinx-1-x-cosx-B-cosx-1-x-sinx-satisfy-the-differential-equation-d-2-y-dx-2-1-2-x-2-y-0-

Question Number 9011 by tawakalitu last updated on 13/Nov/16 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{for}\:\mathrm{any}\:\mathrm{arbitary}\:\mathrm{constants}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B} \\ $$$$\mathrm{y}\:=\:\mathrm{A}\left(\mathrm{sinx}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\mathrm{cosx}\right)\:+\:\mathrm{B}\left(\mathrm{cosx}\:−\:\frac{\mathrm{1}}{\mathrm{x}}\mathrm{sinx}\right)\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}\:\:\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:+\:\left(\mathrm{1}\:−\:\frac{\mathrm{2}}{\mathrm{x}^{\mathrm{2}} }\right)\mathrm{y}\:=\:\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact:…

please-solve-0-f-x-dx-g-x-

Question Number 8798 by javawithfish last updated on 28/Oct/16 $${please}\:{solve} \\ $$$$\int_{\mathrm{0}} ^{\infty} {f}\left({x}\right){dx}={g}\left({x}\right) \\ $$ Commented by Yozzias last updated on 28/Oct/16 $$\mathrm{Impossible}\:\mathrm{unless}\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}\right)=\mathrm{0}\:\forall\mathrm{x}\in\mathbb{R}.\:\mathrm{The}\:\mathrm{definite}\: \\…

Find-the-general-solution-of-the-equation-dy-dx-2xy-y-2-x-2-2xy-

Question Number 8789 by tawakalitu last updated on 27/Oct/16 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{2xy}\:+\:\mathrm{y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2xy}} \\ $$ Commented by Yozzias last updated on 27/Oct/16 $$\mathrm{Let}\:\mathrm{y}=\mathrm{ux}\Rightarrow\mathrm{y}'=\mathrm{u}+\mathrm{xu}' \\…

Question-74142

Question Number 74142 by MASANJAJ last updated on 19/Nov/19 Answered by Rio Michael last updated on 19/Nov/19 $$\:{T}_{\mathrm{7}} \:=\:{a}\:+\:\mathrm{6}{d}\:=\:\mathrm{6}\:−−−\left(\mathrm{1}\right) \\ $$$${T}_{\mathrm{18}} \:=\:{a}\:+\:\mathrm{17}{d}\:=\:\mathrm{22}−−−\left(\mathrm{2}\right) \\ $$$$\:{eqn}\left(\mathrm{2}\right)\:−\:{eqn}\left(\mathrm{1}\right)\:\Rightarrow\:\mathrm{11}{d}\:=\:\mathrm{16} \\…