Question Number 5208 by sanusihammed last updated on 30/Apr/16 $${If}\:{y}\:=\:{x}!\: \\ $$$$ \\ $$$${Find}\:\frac{{dy}}{{dx}} \\ $$ Commented by FilupSmith last updated on 30/Apr/16 $${x}!=\Gamma\left({x}+\mathrm{1}\right) \\…
Question Number 70720 by oyemi kemewari last updated on 07/Oct/19 $$\mathrm{y}''+\frac{\mathrm{y}'}{\mathrm{x}}+\frac{\mathrm{4y}}{\mathrm{x}^{\mathrm{2}} }=\mathrm{1}+\mathrm{x}^{\mathrm{2}} \\ $$ Commented by Rasheed.Sindhi last updated on 07/Oct/19 $$\mathcal{T}{hank}\:{you}! \\ $$ Commented…
Question Number 70694 by oyemi kemewari last updated on 07/Oct/19 Answered by mind is power last updated on 07/Oct/19 $${let}\:\frac{{y}'}{{x}}={u} \\ $$$$\Rightarrow{y}'={xu}\Rightarrow{y}''={u}+{xu}' \\ $$$${xy}''={xu}+{x}^{\mathrm{2}} {u}'…
Question Number 4915 by Yozzii last updated on 21/Mar/16 $${ln}\left(\frac{{d}\left\{{y}\left({x}\right)\right\}}{{dx}}\right)=\frac{{d}}{{dx}}\left({ln}\left\{{y}\left({x}\right)\right\}\right) \\ $$$${y}\left({x}\right)=? \\ $$ Commented by Yozzii last updated on 21/Mar/16 $${y}^{'} =\frac{{d}\left\{{y}\left({x}\right)\right\}}{{dx}} \\ $$$$\Rightarrow{lny}^{'}…
Question Number 70232 by Joel122 last updated on 02/Oct/19 $$\mathrm{Solve} \\ $$$${xy}'\:−\:{y}\:\mathrm{sin}\:{x}\:+\:{y}^{\mathrm{5}} \:=\:\mathrm{0} \\ $$ Commented by Joel122 last updated on 02/Oct/19 $$\mathrm{I}\:\mathrm{think}\:\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{Bernoulli}'\mathrm{s}\:\mathrm{equation} \\ $$$${y}'\:−\:\left(\frac{\mathrm{sin}\:{x}}{{x}}\right){y}\:=\:−\frac{{y}^{\mathrm{5}}…
Question Number 4625 by Yozzis last updated on 14/Feb/16 $${Solve}\:{the}\:{following}\:{system}\:{of}\:{differential}\: \\ $$$${equations}\:{for}\:{functions}\:{x}\left({t}\right)\:{and}\:{y}\left({t}\right). \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}\frac{{d}^{\mathrm{2}} {x}}{{dt}^{\mathrm{2}} }=\frac{{kx}}{\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}\frac{{d}^{\mathrm{2}} {y}}{{dt}^{\mathrm{2}} }=\frac{{ky}}{\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\mathrm{2}}…
Question Number 4472 by Yozzii last updated on 30/Jan/16 $${Solve}\:{the}\:{following}\:{differential}\:{equation}: \\ $$$$\:\:\:\:\:\:\:\:\left(\mathrm{2}{xy}^{\mathrm{2}} +\frac{{x}}{{y}^{\mathrm{2}} }\right){dx}+\mathrm{4}{x}^{\mathrm{2}} {ydy}=\mathrm{0} \\ $$ Commented by prakash jain last updated on 01/Feb/16…
Question Number 135401 by rs4089 last updated on 12/Mar/21 $${find}\:{integrating}\:{factor}\:{or}\:{this}\:{diff}. \\ $$$${equ}^{{n}} \:{for}\:{which}\:{it}\:{become}\:{exact}\: \\ $$$$\left({x}^{\mathrm{2}} −{xy}−{y}^{\mathrm{2}} \right){dy}+{y}^{\mathrm{2}} {dx}=\mathrm{0} \\ $$ Terms of Service Privacy Policy…
Question Number 135173 by bemath last updated on 11/Mar/21 Answered by john_santu last updated on 11/Mar/21 $${Homogenous}\:{problem} \\ $$$${y}_{{h}} '''−{y}_{{h}} ''−\mathrm{2}{y}_{{h}} '\:=\:\mathrm{0} \\ $$$${let}\:{y}_{{h}} \:=\:{e}^{{mx}}…
Question Number 135061 by liberty last updated on 09/Mar/21 $$ \\ $$How can I solve the differential equation (1+x^2)^2y′′+2x(1+x^2)y′+4y=0 Answered by EDWIN88 last updated on 10/Mar/21…