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Question Number 67759 Answers: 0 Comments: 1

using variation of parameters method (x+2)^2 y′′−(x+2)y′=2x+4 x^2 y′′+2xy′−2y=x^2 lnx+3x

$${using}\:{variation}\:{of}\:{parameters}\:{method} \\ $$$$ \\ $$$$\left({x}+\mathrm{2}\right)^{\mathrm{2}} {y}''−\left({x}+\mathrm{2}\right){y}'=\mathrm{2}{x}+\mathrm{4} \\ $$$$ \\ $$$$ \\ $$$${x}^{\mathrm{2}} {y}''+\mathrm{2}{xy}'−\mathrm{2}{y}={x}^{\mathrm{2}} {lnx}+\mathrm{3}{x} \\ $$

Question Number 67761 Answers: 0 Comments: 0

solve by laplace transform method x^(•• ) +w_0 ^2 x=coswt x(0)=x_0 x^• (0)=v_0 w^2 ≠ w_0 ^2

$${solve}\:{by}\:{laplace}\:{transform}\:{method} \\ $$$$ \\ $$$$\overset{\bullet\bullet\:} {{x}}\:+{w}_{\mathrm{0}} ^{\mathrm{2}} {x}={coswt}\:\:\:{x}\left(\mathrm{0}\right)={x}_{\mathrm{0}} \:\overset{\bullet} {{x}}\left(\mathrm{0}\right)={v}_{\mathrm{0}} \:\:\:\:\:{w}^{\mathrm{2}} \neq\:{w}_{\mathrm{0}} ^{\mathrm{2}} \\ $$

Question Number 67762 Answers: 0 Comments: 0

solve by the complex method y^(iv) +3y^3 +2y^2 =−3sin2x y^2 +a^2 y=e^x cosecx

$${solve}\:{by}\:{the}\:{complex}\:{method} \\ $$$$ \\ $$$$ \\ $$$${y}^{{iv}} +\mathrm{3}{y}^{\mathrm{3}} +\mathrm{2}{y}^{\mathrm{2}} =−\mathrm{3}{sin}\mathrm{2}{x} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$${y}^{\mathrm{2}} +{a}^{\mathrm{2}} {y}={e}^{{x}} {cosecx} \\ $$

Question Number 67749 Answers: 1 Comments: 0

Question Number 67745 Answers: 3 Comments: 0

solve the system of equations { ((3∣x−5∣+4=y)),((∣y−3∣=4x−12)) :}

$${solve}\:{the}\:{system}\:{of}\:{equations\begin{cases}{\mathrm{3}\mid{x}−\mathrm{5}\mid+\mathrm{4}={y}}\\{\mid{y}−\mathrm{3}\mid=\mathrm{4}{x}−\mathrm{12}}\end{cases}} \\ $$

Question Number 67744 Answers: 0 Comments: 4

let f(x) =∫_0 ^∞ ((sin(t^2 ))/((x^2 +t^2 )^2 ))dt with x>0 1)determine a explicit form for f(x) 2) find also g(x) =∫_0 ^∞ ((sin(t^2 ))/((x^2 +t^2 )^3 ))dt 3) give f^((n)) (x) at form of integral and calculate f^((n)) (1). 4) find the valueof ∫_0 ^∞ ((sin(t^2 ))/((1+t^2 )^2 )) dt and ∫_0 ^∞ ((sin(t^2 ))/((1+t^2 )^3 ))dt

Question Number 67743 Answers: 0 Comments: 0

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Question Number 67728 Answers: 1 Comments: 5

Question Number 67719 Answers: 1 Comments: 0

Question Number 67716 Answers: 2 Comments: 0

Question Number 67711 Answers: 0 Comments: 0

Find the value of (1/(cos^2 (10°))) + (1/(sin^2 (20°))) + (1/(sin^2 (40°)))

$${Find}\:\:{the}\:\:{value}\:\:{of} \\ $$$$\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{cos}^{\mathrm{2}} \left(\mathrm{10}°\right)}\:+\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{20}°\right)}\:+\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{40}°\right)}\: \\ $$

Question Number 67708 Answers: 1 Comments: 0

Question Number 67698 Answers: 0 Comments: 0

Question Number 67697 Answers: 1 Comments: 0

⋓si⋒g ChineseRemainderTheorm ∂etermine polynomial p(x) such that p(x)≡8(mod x+1) p(x)≡−24(mod x+3) p(x)≡6(mod x) p(x)≡0(mod x+2)

$$\Cup\mathrm{si}\Cap\mathrm{g}\:\mathrm{ChineseRemainderTheorm} \\ $$$$\partial\mathrm{etermine}\:\mathrm{polynomial}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{such}\:\mathrm{that} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{p}\left(\mathrm{x}\right)\equiv\mathrm{8}\left(\mathrm{mod}\:\mathrm{x}+\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:\:\mathrm{p}\left(\mathrm{x}\right)\equiv−\mathrm{24}\left(\mathrm{mod}\:\mathrm{x}+\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\:\:\mathrm{p}\left(\mathrm{x}\right)\equiv\mathrm{6}\left(\mathrm{mod}\:\mathrm{x}\right) \\ $$$$\:\:\:\:\:\:\:\:\mathrm{p}\left(\mathrm{x}\right)\equiv\mathrm{0}\left(\mathrm{mod}\:\mathrm{x}+\mathrm{2}\right) \\ $$$$ \\ $$

Question Number 67696 Answers: 0 Comments: 0

∫_0 ^1 (1−x)/(1+x)lnx dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}\right)/\left(\mathrm{1}+{x}\right){lnx}\:{dx} \\ $$

Question Number 67692 Answers: 1 Comments: 0

Question Number 67688 Answers: 0 Comments: 1

A relation R defined by _((x,y)) R_((u,v)) ⇔ v^2 −y^2 = u^2 −x^2 show that R is an equivalent Relation.

$${A}\:{relation}\:\mathbb{R}\:{defined}\:{by}\:\:\:_{\left({x},{y}\right)} {R}_{\left({u},{v}\right)} \:\Leftrightarrow\:\:{v}^{\mathrm{2}} −{y}^{\mathrm{2}} \:=\:{u}^{\mathrm{2}} −{x}^{\mathrm{2}} \\ $$$${show}\:{that}\:{R}\:{is}\:{an}\:{equivalent}\:{Relation}. \\ $$

Question Number 67687 Answers: 0 Comments: 3

find the range of values of ∣((x^2 −9)/3_ )∣= ((9−x^2 )/3)

$${find}\:{the}\:{range}\:{of}\:{values}\:{of}\: \\ $$$$\:\:\mid\frac{{x}^{\mathrm{2}} −\mathrm{9}}{\mathrm{3}_{\:} }\mid=\:\frac{\mathrm{9}−{x}^{\mathrm{2}} }{\mathrm{3}} \\ $$$$ \\ $$

Question Number 67686 Answers: 0 Comments: 2

given that the roots of the equation 4x^2 + 6x + 9 =0 are λ and δ where λ = (1 + α^2 +β^2 ) and δ = α^3 + β^3 find an equation whose roots are (1/(αλ)) and (1/(βδ))

$${given}\:{that}\:{the}\:{roots}\:{of}\:{the}\:{equation}\:\:\mathrm{4}{x}^{\mathrm{2}} \:+\:\mathrm{6}{x}\:+\:\mathrm{9}\:=\mathrm{0}\:{are}\:\:\lambda\:{and}\:\delta\:\:{where}\: \\ $$$$\:\lambda\:=\:\left(\mathrm{1}\:+\:\alpha^{\mathrm{2}} \:+\beta^{\mathrm{2}} \right)\:\:{and}\:\:\delta\:=\:\alpha^{\mathrm{3}} \:+\:\beta^{\mathrm{3}} \\ $$$${find}\:{an}\:{equation}\:{whose}\:{roots}\:{are}\: \\ $$$$\:\:\frac{\mathrm{1}}{\alpha\lambda}\:{and}\:\:\frac{\mathrm{1}}{\beta\delta} \\ $$

Question Number 67684 Answers: 0 Comments: 2

given the function f(x) = { ((x^2 , for 0≤ x< 2)),((ax + 3, for 2≤ x < 4)) :} is periodic of period 4, and is continuous. a) Find the value of a. b) Find the valu of f(6) c) sketch the graph for y =f(x). help me please, for the graph i don′t know wbere to put y=x^2 and y = ax + 3 and where do i put a closed dot and an open dot.

$${given}\:{the}\:{function}\: \\ $$$${f}\left({x}\right)\:=\begin{cases}{{x}^{\mathrm{2}} \:\:,\:{for}\:\:\:\mathrm{0}\leqslant\:{x}<\:\mathrm{2}}\\{{ax}\:+\:\mathrm{3},\:{for}\:\:\mathrm{2}\leqslant\:{x}\:<\:\mathrm{4}}\end{cases} \\ $$$${is}\:{periodic}\:{of}\:{period}\:\:\mathrm{4},\:{and}\:{is}\:{continuous}. \\ $$$$\left.{a}\right)\:{Find}\:\:{the}\:{value}\:{of}\:\:{a}. \\ $$$$\left.{b}\right)\:{Find}\:{the}\:{valu}\:{of}\:\:{f}\left(\mathrm{6}\right) \\ $$$$\left.{c}\right)\:{sketch}\:{the}\:{graph}\:{for}\:{y}\:={f}\left({x}\right). \\ $$$${help}\:{me}\:{please},\:{for}\:{the}\:{graph}\:{i}\:{don}'{t}\:{know}\:{wbere}\:{to}\:{put}\:\:{y}={x}^{\mathrm{2}} \:{and}\:{y}\:=\:{ax}\:+\:\mathrm{3}\:{and} \\ $$$${where}\:{do}\:{i}\:{put}\:{a}\:{closed}\:\:{dot}\:{and}\:{an}\:{open}\:{dot}. \\ $$$$ \\ $$

Question Number 67674 Answers: 0 Comments: 3

let f(a) =∫_0 ^∞ (dx/((x^2 +1)(x^2 +a))) with a>0 1) determine a explicit form of f(a) 2) calculate g(a) =∫_0 ^∞ (dx/((x^2 +1)(x^2 +a)^2 )) 3)give f^((n)) (a) at form of integral 4)calculate ∫_0 ^∞ (dx/((x^2 +1)(x^2 +3)^2 )) and ∫_0 ^∞ (dx/((x^2 +1)^3 ))

$${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +{a}\right)}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+{a}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right){give}\:{f}^{\left({n}\right)} \left({a}\right)\:{at}\:{form}\:{of}\:{integral} \\ $$$$\left.\mathrm{4}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }\:{and} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 67673 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) (dx/((x^2 −x+1)(x^2 +x+1)))

$${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right)} \\ $$

Question Number 67672 Answers: 0 Comments: 2

decompose the folowing fraction at R(x) 1)F(x)=(x^3 /(1−x^6 )) 2) G(x) =((x^2 +1)/(x^3 (x^2 +x+1)^2 ))

$${decompose}\:{the}\:{folowing}\:\:{fraction}\:{at}\:{R}\left({x}\right) \\ $$$$\left.\mathrm{1}\right){F}\left({x}\right)=\frac{{x}^{\mathrm{3}} }{\mathrm{1}−{x}^{\mathrm{6}} } \\ $$$$\left.\mathrm{2}\right)\:{G}\left({x}\right)\:=\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}^{\mathrm{3}} \left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 67664 Answers: 0 Comments: 2

show that ∃ n ∈ N^(+ ) : sin^n x + cos^n x = 1 and cosh^n x − sinh^n x = 1. Hint: use Induction method.

$${show}\:{that}\:\:\exists\:{n}\:\in\:{N}^{+\:} \::\:\:{sin}^{{n}} {x}\:+\:{cos}^{{n}} {x}\:=\:\mathrm{1}\:{and}\:\:{cosh}^{{n}} {x}\:−\:{sinh}^{{n}} {x}\:=\:\mathrm{1}. \\ $$$$ \\ $$$${Hint}:\:{use}\:{Induction}\:{method}. \\ $$$$ \\ $$

Question Number 67662 Answers: 0 Comments: 2

please explain the fact that ∫(1/x)dx = ln x + k

$${please}\:{explain}\:{the}\:{fact}\:{that}\: \\ $$$$\int\frac{\mathrm{1}}{{x}}{dx}\:=\:{ln}\:{x}\:+\:{k} \\ $$

Question Number 67660 Answers: 1 Comments: 3

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