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Question Number 91020 Answers: 0 Comments: 2

lim_(x→0) (sin x)^(1/x) ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{sin}\:{x}\right)^{\frac{\mathrm{1}}{{x}}} \:?\: \\ $$

Question Number 91018 Answers: 0 Comments: 1

∫_0 ^π ((sin((21x)/2))/(sin(x/2)))dx

$$\int_{\mathrm{0}} ^{\pi} \frac{{sin}\frac{\mathrm{21}{x}}{\mathrm{2}}}{{sin}\frac{{x}}{\mathrm{2}}}{dx} \\ $$

Question Number 91012 Answers: 1 Comments: 0

(dy/dx) + 2xy = xe^(−x^2 ) y^3

$$\frac{{dy}}{{dx}}\:+\:\mathrm{2}{xy}\:=\:{xe}^{−{x}^{\mathrm{2}} } {y}^{\mathrm{3}} \\ $$

Question Number 91011 Answers: 2 Comments: 0

how to make the sigma and prod sign bigger?

$$\:\mathrm{how}\:\mathrm{to}\:\mathrm{make}\:\mathrm{the}\:\mathrm{sigma}\:\mathrm{and}\:\mathrm{prod}\:\mathrm{sign}\:\mathrm{bigger}? \\ $$

Question Number 91010 Answers: 1 Comments: 2

solve the diff eq y′′′−y′′+4y′−4y= e^x

$${solve}\:{the}\:{diff}\:{eq}\: \\ $$$${y}'''−{y}''+\mathrm{4}{y}'−\mathrm{4}{y}=\:{e}^{{x}} \\ $$

Question Number 91000 Answers: 0 Comments: 2

Solve the differential equations: (d^2 y/dx^2 )+ (x/(1−x^2 )) (dy/dx)− (y/(1−x^2 ))= x(√(1−x^2 ))

Question Number 90997 Answers: 0 Comments: 3

∫ _0 ^π ((sin x dx)/(1+sin x))

$$\int\underset{\mathrm{0}} {\overset{\pi} {\:}}\:\frac{\mathrm{sin}\:{x}\:{dx}}{\mathrm{1}+\mathrm{sin}\:{x}} \\ $$

Question Number 90989 Answers: 1 Comments: 1

Question Number 90983 Answers: 0 Comments: 1

y′′−5y′+6y=x^2

$${y}''−\mathrm{5}{y}'+\mathrm{6}{y}={x}^{\mathrm{2}} \\ $$

Question Number 91068 Answers: 1 Comments: 0

Find the sum (√(1+(1/2^2 )+(1/3^2 )))+(√(1+(1/3^2 )+(1/4^2 )))+...+(√(1+(1/(999^2 ))+(1/(1000^2 ))))

$${Find}\:{the}\:{sum} \\ $$$$\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }}+\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{2}} }}+...+\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{999}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{1000}^{\mathrm{2}} }} \\ $$

Question Number 90974 Answers: 0 Comments: 0

solve cost y^(′′) −2sint y^′ +2cost y =e^t

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

Question Number 90973 Answers: 1 Comments: 2

solve xy^′ +(x+1)y =e^(−x) ln(1+x^2 )

$${solve}\:{xy}^{'} \:+\left({x}+\mathrm{1}\right){y}\:={e}^{−{x}} {ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right) \\ $$

Question Number 90972 Answers: 1 Comments: 0

solve y^(′′) +y =(2/(sin^2 t))

$${solve}\:{y}^{''} \:+{y}\:=\frac{\mathrm{2}}{{sin}^{\mathrm{2}} {t}} \\ $$

Question Number 90971 Answers: 0 Comments: 0

solve y^(′′) +y^′ +y =(e^(−t) /(ch^2 t))

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

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

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

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