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Category: Differential Equation

Consider-the-differential-equation-x-t-x-t-t-2-cos-2t-Knowing-that-the-Complementary-Function-is-y-CF-acos-t-bsin-t-In-what-form-can-the-particular-integral-be-expressed-so-as-to-obtain-

Question Number 104651 by Ar Brandon last updated on 23/Jul/20 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}; \\ $$$$\mathrm{x}''\left(\mathrm{t}\right)+\mathrm{x}\left(\mathrm{t}\right)=\mathrm{t}^{\mathrm{2}} \mathrm{cos}\left(\mathrm{2t}\right). \\ $$$$\mathrm{Knowing}\:\mathrm{that}\:\mathrm{the}\:\mathrm{Complementary}\:\mathrm{Function}\:\mathrm{is}; \\ $$$$\mathrm{y}_{\mathrm{CF}} =\mathrm{acos}\left(\mathrm{t}\right)+\mathrm{bsin}\left(\mathrm{t}\right), \\ $$$$\mathrm{In}\:\mathrm{what}\:\mathrm{form}\:\mathrm{can}\:\mathrm{the}\:\mathrm{particular}\:\mathrm{integral}\:\mathrm{be}\:\mathrm{expressed} \\ $$$$\mathrm{so}\:\mathrm{as}\:\mathrm{to}\:\mathrm{obtain}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{the}\:\mathrm{given}\: \\ $$$$\mathrm{differential}\:\mathrm{equation}?…

solve-d-2-y-dx-2-2x-dy-dx-5y-0-

Question Number 38876 by tawa tawa last updated on 30/Jun/18 $$\mathrm{solve}:\:\:\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:\:+\:\:\mathrm{2x}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:+\:\mathrm{5y}\:=\:\mathrm{0} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 01/Jul/18 $${it}\:{is}\:{realy}\:{very}\:{good}\:{problem}…{in}\:{search}..{and} \\ $$$${finding}\:{way}\:{to}\:{solve}\:{it}……

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

Question Number 104357 by bemath last updated on 21/Jul/20 $$\left({x}+{y}+\mathrm{1}\right)\:\frac{{dy}}{{dx}}\:=\:\mathrm{1}\: \\ $$ Answered by john santu last updated on 21/Jul/20 $${let}\:{z}\:=\:{x}+{y}+\mathrm{1} \\ $$$$\frac{{dz}}{{dx}}\:=\:\mathrm{1}+\:\frac{{dy}}{{dx}}\:\Rightarrow\frac{{dy}}{{dx}}\:=\:\frac{{dz}}{{dx}}−\mathrm{1} \\ $$$$\left(\rightarrow\right)\:{z}.\left(\frac{{dz}}{{dx}}−\mathrm{1}\right)\:=\:\mathrm{1}\:…