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Category: Differential Equation

df-dt-f-t-f-t-

Question Number 1898 by 123456 last updated on 22/Oct/15 $$\frac{{df}}{{dt}}=\alpha{f}+\beta{t}+\gamma \\ $$$${f}\left({t}\right)=?? \\ $$ Answered by Yozzy last updated on 22/Oct/15 $$\frac{{df}}{{dt}}=\alpha{f}+\beta{t}+\gamma\:\:\:{where}\:{I}\:{assume}\:{that}\:\alpha,\beta,\gamma\:{are}\:{constants}.\:{This}\:{equation}\:{may}\:{be} \\ $$$${rewritten}\:{as}\:\:\:\:\:\frac{{df}}{{dt}}−\alpha{f}=\beta{t}+\gamma\:\:\left(\ast\right).\:{The}\:{equation}\:{is}\:{a}\:{first}\:{order}\:{linear}\:{non}−{homogeneous} \\…

find-the-series-solution-of-the-ordinary-differential-equation-y-2-2xy-1-3y-x-2-1-y-0-1-and-y-1-0-2-

Question Number 132881 by Engr_Jidda last updated on 17/Feb/21 $${find}\:{the}\:{series}\:{solution}\:{of} \\ $$$${the}\:{ordinary}\:{differential}\:{equation} \\ $$$${y}^{\mathrm{2}} +\mathrm{2}{xy}^{\mathrm{1}} −\mathrm{3}{y}={x}^{\mathrm{2}} −\mathrm{1} \\ $$$${y}\left(\mathrm{0}\right)=\mathrm{1}\:{and}\:{y}^{\mathrm{1}} \left(\mathrm{0}\right)=\mathrm{2} \\ $$ Terms of Service…

f-x-f-x-dx-ln-sec-x-c-f-x-

Question Number 1597 by Rasheed Ahmad last updated on 25/Aug/15 $$\int\frac{{f}\left({x}\right)}{{f}\:'\left({x}\right)}{dx}={ln}\:{sec}\:{x}+{c} \\ $$$${f}\left({x}\right)=? \\ $$ Answered by 123456 last updated on 25/Aug/15 $$\int\frac{{y}}{{dy}/{dx}}{dx}=\mathrm{ln}\:\mathrm{sec}\:{x}+{c} \\ $$$$\frac{{d}}{{dx}}\left[\int\frac{{y}}{{dy}/{dx}}{dx}\right]=\frac{{d}}{{dx}}\left[\mathrm{ln}\:\mathrm{sec}\:{x}+{c}\right]…

Solve-the-following-D-E-dy-dx-2-2y-2-0-Does-d-2-y-dx-2-2-2y-2-0-have-any-solutions-other-than-y-1-

Question Number 1575 by 112358 last updated on 21/Aug/15 $${Solve}\:{the}\:{following}\:{D}.{E}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} +\mathrm{2}{y}+\mathrm{2}=\mathrm{0}\: \\ $$$${Does}\:\:\left(\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\right)^{\mathrm{2}} +\mathrm{2}{y}+\mathrm{2}=\mathrm{0}\:{have} \\ $$$${any}\:{solutions}\:{other}\:{than} \\ $$$${y}=−\mathrm{1}\:? \\ $$ Commented…