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Question Number 90970 Answers: 0 Comments: 2

find all functions f (2×derivable) verify (f^′ (x))^2 −(f(x))^2 =1 and f^′ (0)=1

$${find}\:{all}\:{functions}\:{f}\:\:\left(\mathrm{2}×{derivable}\right)\:{verify} \\ $$$$\left({f}^{'} \left({x}\right)\right)^{\mathrm{2}} \:−\left({f}\left({x}\right)\right)^{\mathrm{2}} \:=\mathrm{1}\:{and}\:{f}^{'} \left(\mathrm{0}\right)=\mathrm{1} \\ $$

Question Number 90969 Answers: 0 Comments: 3

solve y^(′′) −2ay^′ +(1+a^2 )y =x +e^(ax) a real

$${solve}\:{y}^{''} −\mathrm{2}{ay}^{'} \:+\left(\mathrm{1}+{a}^{\mathrm{2}} \right){y}\:={x}\:+{e}^{{ax}} \\ $$$${a}\:{real} \\ $$

Question Number 90968 Answers: 0 Comments: 2

solve (1+e^x )y^′ −y =(e^x /(1+x^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^(−2x)

$${solve}\:{y}^{''} \:+{y}'\:+{y}\:={xsinx}\:{e}^{−\mathrm{2}{x}} \\ $$

Question Number 90966 Answers: 0 Comments: 4

solve y^(′′) +3y^′ +2 =t−e^(−t) +sint

$${solve}\:\:{y}^{''} \:+\mathrm{3}{y}^{'} +\mathrm{2}\:={t}−{e}^{−{t}} \:+{sint} \\ $$

Question Number 90965 Answers: 0 Comments: 0

solve the (de) ch(x)y^′ +sh(x)y =xe^(−x)

$${solve}\:{the}\:\left({de}\right)\:\:{ch}\left({x}\right){y}^{'} \:+{sh}\left({x}\right){y}\:={xe}^{−{x}} \\ $$

Question Number 90964 Answers: 0 Comments: 0

determine a diff.equation with roots e^(2x) and e^(−x)

$${determine}\:{a}\:{diff}.{equation}\:{with}\:{roots}\:{e}^{\mathrm{2}{x}} \:{and}\:{e}^{−{x}} \\ $$

Question Number 90963 Answers: 1 Comments: 2

solve (1+x^2 )y^′ +xy =(√(1+x^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(x) =x^3 cos(2x) calculate f^((n)) (x) and f^((n)) (0)

$${let}\:{f}\left({x}\right)\:={x}^{\mathrm{3}} {cos}\left(\mathrm{2}{x}\right) \\ $$$${calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$

Question Number 90958 Answers: 0 Comments: 0

let f(z) =(3/(zsin(z^2 ))) calculate Res(f,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′′−5y′−24y=e^(3x)

$${y}''−\mathrm{5}{y}'−\mathrm{24}{y}={e}^{\mathrm{3}{x}} \\ $$$$ \\ $$

Question Number 90954 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((1−e^(−x^2 ) )/x^2 )dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{1}−{e}^{−{x}^{\mathrm{2}} } }{{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 90952 Answers: 1 Comments: 0

solve diff equation x^2 y′′ + xy′ +y = 5x^2 x >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 α^(13) =1 and α≠1,find the quadratic equation whose roots are (α+α^3 +α^4 +α^(−4) +α^(−3) +α^(−1) ) and (α^2 +α^5 +α^6 +α^(−6) +α^(−5) +α^(−6) )

$${if}\:\alpha^{\mathrm{13}} =\mathrm{1}\:{and}\:\alpha\neq\mathrm{1},{find}\:{the}\:{quadratic}\:\:{equation} \\ $$$${whose}\:{roots}\:{are}\:\left(\alpha+\alpha^{\mathrm{3}} +\alpha^{\mathrm{4}} +\alpha^{−\mathrm{4}} +\alpha^{−\mathrm{3}} +\alpha^{−\mathrm{1}} \right)\:{and}\:\left(\alpha^{\mathrm{2}} +\alpha^{\mathrm{5}} +\alpha^{\mathrm{6}} +\alpha^{−\mathrm{6}} +\alpha^{−\mathrm{5}} +\alpha^{−\mathrm{6}} \right) \\ $$

Question Number 90946 Answers: 0 Comments: 0

determine x,y,z ∈ R such that 2x^2 +y^2 +2z^2 −8x+2y−2xy+2xz−16z+35=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

lim_(x→0) ((x sin x)/(2sin^2 3x−x^2 cos x)) ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\:\mathrm{sin}\:{x}}{\mathrm{2sin}\:^{\mathrm{2}} \mathrm{3}{x}−{x}^{\mathrm{2}} \:\mathrm{cos}\:{x}}\:? \\ $$

Question Number 90940 Answers: 1 Comments: 0

f(x)=(x)^(1/3) is there an inflection point when x=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

∫(dx/(sin(x)+cos(x)+tan(x)+cot(x)+sec(x)+csc(x)))

$$\int\frac{{dx}}{{sin}\left({x}\right)+{cos}\left({x}\right)+{tan}\left({x}\right)+{cot}\left({x}\right)+{sec}\left({x}\right)+{csc}\left({x}\right)} \\ $$

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.

$${do}\:{you}\:{all}\:{get}\:{notifications}\:{when} \\ $$$${your}\:{posts}\:{get}\:{updated}? \\ $$$${i}\:{don}'{t}\:{get}\:{any}\:{notification}.\:{so}\:{i}\:{don}'{t} \\ $$$${know}\:{if}\:{a}\:{post}\:{of}\:{mine}\:{is}\:{updated}\:{or} \\ $$$${not},\:{very}\:{uncomfortable}. \\ $$

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

(dy/dx) −((4y)/x) = 1+(2/x)

$$\frac{{dy}}{{dx}}\:−\frac{\mathrm{4}{y}}{{x}}\:=\:\mathrm{1}+\frac{\mathrm{2}}{{x}} \\ $$

Question Number 90881 Answers: 2 Comments: 6

if the value of x is in degrees what is the derivative of f(x)=sin(x)

$${if}\:{the}\:{value}\:{of}\:{x}\:{is}\:{in}\:{degrees}\:{what}\:{is} \\ $$$${the}\:{derivative}\:{of}\:\:\:{f}\left({x}\right)={sin}\left({x}\right) \\ $$

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