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Question Number 90970 Answers: 0 Comments: 2
$${find}\:{all}\:{functions}\:{f}\:\:\left(\mathrm{2}×{derivable}\right)\:{verify} \\ $$$$\left({f}^{'} \left({x}\right)\right)^{\mathrm{2}} \:−\left({f}\left({x}\right)\right)^{\mathrm{2}} \:=\mathrm{1}\:{and}\:{f}^{'} \left(\mathrm{0}\right)=\mathrm{1} \\ $$
Question Number 90969 Answers: 0 Comments: 3
$${solve}\:{y}^{''} −\mathrm{2}{ay}^{'} \:+\left(\mathrm{1}+{a}^{\mathrm{2}} \right){y}\:={x}\:+{e}^{{ax}} \\ $$$${a}\:{real} \\ $$
Question Number 90968 Answers: 0 Comments: 2
$${solve}\:\left(\mathrm{1}+{e}^{{x}} \right){y}^{'} −{y}\:=\frac{{e}^{{x}} }{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$
Question Number 90967 Answers: 0 Comments: 0
$${solve}\:{y}^{''} \:+{y}'\:+{y}\:={xsinx}\:{e}^{−\mathrm{2}{x}} \\ $$
Question Number 90966 Answers: 0 Comments: 4
$${solve}\:\:{y}^{''} \:+\mathrm{3}{y}^{'} +\mathrm{2}\:={t}−{e}^{−{t}} \:+{sint} \\ $$
Question Number 90965 Answers: 0 Comments: 0
$${solve}\:{the}\:\left({de}\right)\:\:{ch}\left({x}\right){y}^{'} \:+{sh}\left({x}\right){y}\:={xe}^{−{x}} \\ $$
Question Number 90964 Answers: 0 Comments: 0
$${determine}\:{a}\:{diff}.{equation}\:{with}\:{roots}\:{e}^{\mathrm{2}{x}} \:{and}\:{e}^{−{x}} \\ $$
Question Number 90963 Answers: 1 Comments: 2
$${solve}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{'} \:+{xy}\:=\sqrt{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$
Question Number 90960 Answers: 1 Comments: 2
$${let}\:{f}\left({x}\right)\:={x}^{\mathrm{3}} {cos}\left(\mathrm{2}{x}\right) \\ $$$${calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$
Question Number 90958 Answers: 0 Comments: 0
$${let}\:{f}\left({z}\right)\:=\frac{\mathrm{3}}{{zsin}\left({z}^{\mathrm{2}} \right)} \\ $$$${calculate}\:{Res}\left({f},\mathrm{0}\right) \\ $$
Question Number 90955 Answers: 0 Comments: 6
$${y}''−\mathrm{5}{y}'−\mathrm{24}{y}={e}^{\mathrm{3}{x}} \\ $$$$ \\ $$
Question Number 90954 Answers: 0 Comments: 0
$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{1}−{e}^{−{x}^{\mathrm{2}} } }{{x}^{\mathrm{2}} }{dx} \\ $$
Question Number 90952 Answers: 1 Comments: 0
$$ \\ $$$${solve}\:{diff}\:{equation}\: \\ $$$${x}^{\mathrm{2}} {y}''\:+\:{xy}'\:+{y}\:=\:\mathrm{5}{x}^{\mathrm{2}} \:\:{x}\:>\mathrm{0} \\ $$
Question Number 90948 Answers: 2 Comments: 2
Question Number 90947 Answers: 0 Comments: 0
$${if}\:\alpha^{\mathrm{13}} =\mathrm{1}\:{and}\:\alpha\neq\mathrm{1},{find}\:{the}\:{quadratic}\:\:{equation} \\ $$$${whose}\:{roots}\:{are}\:\left(\alpha+\alpha^{\mathrm{3}} +\alpha^{\mathrm{4}} +\alpha^{−\mathrm{4}} +\alpha^{−\mathrm{3}} +\alpha^{−\mathrm{1}} \right)\:{and}\:\left(\alpha^{\mathrm{2}} +\alpha^{\mathrm{5}} +\alpha^{\mathrm{6}} +\alpha^{−\mathrm{6}} +\alpha^{−\mathrm{5}} +\alpha^{−\mathrm{6}} \right) \\ $$
Question Number 90946 Answers: 0 Comments: 0
$${determine}\:{x},{y},{z}\:\in\:\mathbb{R}\:{such}\:{that}\: \\ $$$$\mathrm{2}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{2}{z}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{2}{y}−\mathrm{2}{xy}+\mathrm{2}{xz}−\mathrm{16}{z}+\mathrm{35}=\mathrm{0} \\ $$
Question Number 90944 Answers: 0 Comments: 3
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\:\mathrm{sin}\:{x}}{\mathrm{2sin}\:^{\mathrm{2}} \mathrm{3}{x}−{x}^{\mathrm{2}} \:\mathrm{cos}\:{x}}\:? \\ $$
Question Number 90940 Answers: 1 Comments: 0
$${f}\left({x}\right)=\sqrt[{\mathrm{3}}]{{x}}\:\:{is}\:{there}\:{an}\:{inflection}\:{point} \\ $$$${when}\:{x}=\mathrm{0} \\ $$
Question Number 90938 Answers: 0 Comments: 0
$$\int\frac{{dx}}{{sin}\left({x}\right)+{cos}\left({x}\right)+{tan}\left({x}\right)+{cot}\left({x}\right)+{sec}\left({x}\right)+{csc}\left({x}\right)} \\ $$
Question Number 90923 Answers: 1 Comments: 1
Question Number 90918 Answers: 0 Comments: 1
$${do}\:{you}\:{all}\:{get}\:{notifications}\:{when} \\ $$$${your}\:{posts}\:{get}\:{updated}? \\ $$$${i}\:{don}'{t}\:{get}\:{any}\:{notification}.\:{so}\:{i}\:{don}'{t} \\ $$$${know}\:{if}\:{a}\:{post}\:{of}\:{mine}\:{is}\:{updated}\:{or} \\ $$$${not},\:{very}\:{uncomfortable}. \\ $$
Question Number 90916 Answers: 0 Comments: 0
Question Number 90914 Answers: 0 Comments: 2
Question Number 90911 Answers: 0 Comments: 3
Question Number 90886 Answers: 1 Comments: 0
$$\frac{{dy}}{{dx}}\:−\frac{\mathrm{4}{y}}{{x}}\:=\:\mathrm{1}+\frac{\mathrm{2}}{{x}} \\ $$
Question Number 90881 Answers: 2 Comments: 6
$${if}\:{the}\:{value}\:{of}\:{x}\:{is}\:{in}\:{degrees}\:{what}\:{is} \\ $$$${the}\:{derivative}\:{of}\:\:\:{f}\left({x}\right)={sin}\left({x}\right) \\ $$
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