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Category: Differential Equation

Question-74821

Question Number 74821 by sridhar nayak last updated on 01/Dec/19 Answered by mind is power last updated on 01/Dec/19 $$\Leftrightarrow\left(\mathrm{6e}^{\mathrm{y}} −\mathrm{2x}\right)\mathrm{dy}−\mathrm{dx}=\mathrm{0}…\mathrm{E} \\ $$$$\mathrm{try}\:\mathrm{too}\:\mathrm{find}\:\mathrm{k}\left(\mathrm{y}\right)\:\mathrm{To}\:\mathrm{mak}\:\mathrm{it}\:\mathrm{exacte} \\ $$$$\Leftrightarrow\mathrm{k}\left(\mathrm{y}\right)\left(\mathrm{6e}^{\mathrm{y}}…

Solve-x-2-1-dy-4x-xy-2-dx-y-0-2-

Question Number 9226 by tawakalitu last updated on 24/Nov/16 $$\mathrm{Solve}:\:\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}\right)\mathrm{dy}\:=\:\left(\mathrm{4x}\:+\:\mathrm{xy}^{\mathrm{2}} \right)\mathrm{dx} \\ $$$$\mathrm{y}\left(\mathrm{0}\right)\:=\:\mathrm{2} \\ $$ Answered by mrW last updated on 24/Nov/16 $$\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\mathrm{dy}=\mathrm{x}\left(\mathrm{4}+\mathrm{y}^{\mathrm{2}}…

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}' \\…