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Question Number 77605 Answers: 0 Comments: 0

how to solve : y′′+p(x)y′+q(x)y=r(x)

$$\mathrm{how}\:\mathrm{to}\:\mathrm{solve}\:: \\ $$$$\mathrm{y}''+\mathrm{p}\left(\mathrm{x}\right)\mathrm{y}'+\mathrm{q}\left(\mathrm{x}\right)\mathrm{y}=\mathrm{r}\left(\mathrm{x}\right) \\ $$

Question Number 77604 Answers: 2 Comments: 0

given (((a−b)(b−c)(c−a))/((a+b)(b+c)(c+a)))=−(1/(30)) what the value of (b/(a+b))+(c/(b+c))+(a/(c+a)) ?

$${given} \\ $$$$\frac{\left({a}−{b}\right)\left({b}−{c}\right)\left({c}−{a}\right)}{\left({a}+{b}\right)\left({b}+{c}\right)\left({c}+{a}\right)}=−\frac{\mathrm{1}}{\mathrm{30}} \\ $$$${what}\:{the}\:{value}\:{of}\: \\ $$$$\frac{{b}}{{a}+{b}}+\frac{{c}}{{b}+{c}}+\frac{{a}}{{c}+{a}}\:? \\ $$

Question Number 77603 Answers: 1 Comments: 1

∫((10x^2 −8x+1)/(x^4 −x^3 −x+1))dx

$$\int\frac{\mathrm{10}{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{1}}{{x}^{\mathrm{4}} −{x}^{\mathrm{3}} −{x}+\mathrm{1}}{dx} \\ $$$$ \\ $$

Question Number 77593 Answers: 0 Comments: 10

Question Number 77591 Answers: 1 Comments: 5

x + (1/x) = 1 x^(100) + (1/x^(100) ) = ? x^(2020) + (1/x^(2020) ) = ?

$${x}\:+\:\frac{\mathrm{1}}{{x}}\:\:=\:\:\mathrm{1} \\ $$$${x}^{\mathrm{100}} \:+\:\frac{\mathrm{1}}{{x}^{\mathrm{100}} }\:\:=\:\:? \\ $$$${x}^{\mathrm{2020}} \:+\:\frac{\mathrm{1}}{{x}^{\mathrm{2020}} }\:\:=\:\:? \\ $$

Question Number 77574 Answers: 0 Comments: 9

what is maximum value of y= (3x+4)^2 ×sin (2x)

$${what}\:{is}\:{maximum}\: \\ $$$${value}\:{of}\:{y}=\:\left(\mathrm{3}{x}+\mathrm{4}\right)^{\mathrm{2}} ×\mathrm{sin}\:\left(\mathrm{2}{x}\right) \\ $$

Question Number 77573 Answers: 0 Comments: 2

xln x =((143851)/(40000)) solve for x ⇒ nice surprise

$${x}\mathrm{ln}\:{x}\:=\frac{\mathrm{143851}}{\mathrm{40000}} \\ $$$$\mathrm{solve}\:\mathrm{for}\:{x}\:\Rightarrow\:\mathrm{nice}\:\mathrm{surprise} \\ $$

Question Number 77570 Answers: 1 Comments: 0

∫_( 0) ^( 1) log(((1 + x + x^2 + x^3 + x^4 )/(√(1 + (1/x) + (1/x^2 ) + (1/x^3 ) + (1/x^4 ))))) dx

$$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\:\mathrm{log}\left(\frac{\mathrm{1}\:+\:\mathrm{x}\:+\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{x}^{\mathrm{4}} }{\sqrt{\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} }}}\right)\:\mathrm{dx} \\ $$

Question Number 77565 Answers: 0 Comments: 6

Question Number 77556 Answers: 0 Comments: 2

1. 1×1!×2!+2×2!×3!+3×3!×4!+....=? 2. ((1+(√2))/(2+(√3)))+((2+(√3))/(3+(√4)))+((3+(√4))/(4+(√5)))+......=? 3. (1/(1+(√2)+(√3)))+(2/((√2)+(√3)+(√4)))+(3/((√3)+(√4)+(√5)))+....=?

$$\mathrm{1}.\:\:\:\mathrm{1}×\mathrm{1}!×\mathrm{2}!+\mathrm{2}×\mathrm{2}!×\mathrm{3}!+\mathrm{3}×\mathrm{3}!×\mathrm{4}!+....=? \\ $$$$\mathrm{2}.\:\:\:\:\frac{\mathrm{1}+\sqrt{\mathrm{2}}}{\mathrm{2}+\sqrt{\mathrm{3}}}+\frac{\mathrm{2}+\sqrt{\mathrm{3}}}{\mathrm{3}+\sqrt{\mathrm{4}}}+\frac{\mathrm{3}+\sqrt{\mathrm{4}}}{\mathrm{4}+\sqrt{\mathrm{5}}}+......=? \\ $$$$\mathrm{3}.\:\:\:\frac{\mathrm{1}}{\mathrm{1}+\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}}+\frac{\mathrm{2}}{\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}}+\frac{\mathrm{3}}{\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}+\sqrt{\mathrm{5}}}+....=?\: \\ $$

Question Number 77552 Answers: 1 Comments: 0

∫((x−2)/(x^2 −x+1))dx = ?

$$\int\frac{\mathrm{x}−\mathrm{2}}{\mathrm{x}^{\mathrm{2}} −{x}+\mathrm{1}}{dx}\:=\:? \\ $$

Question Number 77554 Answers: 0 Comments: 1

Question Number 77549 Answers: 0 Comments: 2

Question Number 77545 Answers: 0 Comments: 0

Question Number 77539 Answers: 0 Comments: 11

Question Number 77537 Answers: 1 Comments: 0

what is the solution xy′+(1+xcot x)y=x ?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{solution}\: \\ $$$$\mathrm{xy}'+\left(\mathrm{1}+\mathrm{xcot}\:\mathrm{x}\right)\mathrm{y}=\mathrm{x}\:? \\ $$

Question Number 77536 Answers: 1 Comments: 0

find all function that satisfy ∀ p>0 ∫_0 ^∞ f(t)e^(−pt) dt= e^(−pT) with T a positive real

$$\mathrm{find}\:\mathrm{all}\:\mathrm{function}\:\mathrm{that}\:\mathrm{satisfy} \\ $$$$\:\:\forall\:\mathrm{p}>\mathrm{0}\:\:\:\int_{\mathrm{0}} ^{\infty} \mathrm{f}\left(\mathrm{t}\right)\mathrm{e}^{−\mathrm{pt}} \mathrm{dt}=\:\mathrm{e}^{−\mathrm{pT}} \:\:\:\:\:\:\mathrm{with}\:\mathrm{T}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{real} \\ $$

Question Number 77533 Answers: 1 Comments: 0

If f(x)=x sin((1/x)) where x≠0 then find the value of function at x=0 and given that function is continuous at x=0 ?

$$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}\:\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:\mathrm{where}\:\mathrm{x}\neq\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{function}\:\mathrm{at}\:\mathrm{x}=\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{given}\:\mathrm{that}\:\mathrm{function}\:\mathrm{is}\:\mathrm{continuous}\:\mathrm{at}\:\mathrm{x}=\mathrm{0}\:? \\ $$

Question Number 77528 Answers: 0 Comments: 0

Σ_(k=1) ^∞ (k^α /2^k )=?

$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{k}^{\alpha} }{\mathrm{2}^{{k}} }=? \\ $$

Question Number 77524 Answers: 1 Comments: 2

Question Number 77523 Answers: 0 Comments: 0

how many silly questions can a person ask within the first δ days of the year ψ when the number χ_0 of his IDs∉R in the year ψ−1 is given by [ln ((ψ/2)+3M)]≤χ_0 <lim_(q_0 , x→∞) ((q_0 ^x (√(2πx)))/e^q_0 ) where M is the duration of a month measured in ((hr)/(24)) and (ψ−2)^2 +δ^3 is prime?

$$\mathrm{how}\:\mathrm{many}\:\mathrm{silly}\:\mathrm{questions}\:\mathrm{can}\:\mathrm{a}\:\mathrm{person}\:\mathrm{ask} \\ $$$$\mathrm{within}\:\mathrm{the}\:\mathrm{first}\:\delta\:\mathrm{days}\:\mathrm{of}\:\mathrm{the}\:\mathrm{year}\:\psi\:\mathrm{when} \\ $$$$\mathrm{the}\:\mathrm{number}\:\chi_{\mathrm{0}} \:\mathrm{of}\:\mathrm{his}\:\mathrm{IDs}\notin\mathbb{R}\:\mathrm{in}\:\mathrm{the}\:\mathrm{year}\:\psi−\mathrm{1} \\ $$$$\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\left[\mathrm{ln}\:\left(\frac{\psi}{\mathrm{2}}+\mathrm{3}\mathbb{M}\right)\right]\leqslant\chi_{\mathrm{0}} <\underset{{q}_{\mathrm{0}} ,\:{x}\rightarrow\infty} {\mathrm{lim}}\frac{{q}_{\mathrm{0}} ^{{x}} \sqrt{\mathrm{2}\pi{x}}}{\mathrm{e}^{{q}_{\mathrm{0}} } } \\ $$$$\mathrm{where}\:\mathbb{M}\:\mathrm{is}\:\mathrm{the}\:\mathrm{duration}\:\mathrm{of}\:\mathrm{a}\:\mathrm{month}\:\mathrm{measured} \\ $$$$\mathrm{in}\:\frac{\mathrm{hr}}{\mathrm{24}}\:\mathrm{and}\:\left(\psi−\mathrm{2}\right)^{\mathrm{2}} +\delta^{\mathrm{3}} \:\mathrm{is}\:\mathrm{prime}? \\ $$

Question Number 77514 Answers: 2 Comments: 0

Question Number 77513 Answers: 0 Comments: 3

Question Number 77506 Answers: 1 Comments: 2

Question Number 77505 Answers: 1 Comments: 1

many three digit multiples of three that can be made from the number 0,1,2,3,4,5,6,7 without repetition?

$${many}\:{three}\: \\ $$$${digit}\:{multiples}\:{of}\:{three}\:{that} \\ $$$${can}\:{be}\:{made}\:{from}\:{the}\:{number} \\ $$$$\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7}\:{without}\:{repetition}? \\ $$

Question Number 77504 Answers: 1 Comments: 0

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