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AllQuestion and Answers: Page 1222

Question Number 91850 Answers: 0 Comments: 3

Question Number 91848 Answers: 0 Comments: 1

y^(′′) −4y^′ +4y=(x+1)e^(2x)

$${y}^{''} −\mathrm{4}{y}^{'} +\mathrm{4}{y}=\left({x}+\mathrm{1}\right){e}^{\mathrm{2}{x}} \\ $$$$ \\ $$

Question Number 91844 Answers: 0 Comments: 5

Question Number 91843 Answers: 2 Comments: 5

{ (((1/x)+y = 2)),((x+(1/y) = 3)) :} find x^2 +y^2

$$\begin{cases}{\frac{\mathrm{1}}{{x}}+{y}\:=\:\mathrm{2}}\\{{x}+\frac{\mathrm{1}}{{y}}\:=\:\mathrm{3}}\end{cases} \\ $$$${find}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$

Question Number 91842 Answers: 1 Comments: 1

∫ (dx/(x(√(4x^2 +2x−1)))) ?

$$\int\:\frac{{dx}}{{x}\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}}}\:? \\ $$

Question Number 91840 Answers: 0 Comments: 0

solve y y′′=(y′)^2 +y′(√(y^2 +(y′)^2 ))

$${solve}\: \\ $$$${y}\:{y}''=\left({y}'\right)^{\mathrm{2}} +{y}'\sqrt{{y}^{\mathrm{2}} +\left({y}'\right)^{\mathrm{2}} } \\ $$

Question Number 91837 Answers: 0 Comments: 5

1). Σ_(n=1) ^∞ ((5/(n+2))−(5/(n+3)) )=... 2). Σ_(n=1) ^∞ ((1/(4n^2 −1)))=... 3). Σ_(n=1) ^∞ (((3n)/(5n−1)) )=... Σ_(n=1) ^∞ ((n/(n+1)) )=...

$$\left.\mathrm{1}\right).\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{5}}{\mathrm{n}+\mathrm{2}}−\frac{\mathrm{5}}{\mathrm{n}+\mathrm{3}}\:\right)=... \\ $$$$ \\ $$$$\left.\mathrm{2}\right).\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{4n}^{\mathrm{2}} −\mathrm{1}}\right)=... \\ $$$$ \\ $$$$\left.\mathrm{3}\right).\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{3n}}{\mathrm{5n}−\mathrm{1}}\:\right)=... \\ $$$$ \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{n}}{\mathrm{n}+\mathrm{1}}\:\right)=... \\ $$

Question Number 91836 Answers: 1 Comments: 1

Question Number 91825 Answers: 2 Comments: 3

(cos x) (dy/dx)−y(sin x) = cot (x)

$$\left(\mathrm{cos}\:{x}\right)\:\frac{{dy}}{{dx}}−{y}\left(\mathrm{sin}\:{x}\right)\:=\:\mathrm{cot}\:\left({x}\right) \\ $$

Question Number 92524 Answers: 0 Comments: 0

(d^3 x/dt^3 ) + 27 (d^2 x/dt^2 ) + 243 (dx/dt) + 729x = t∙ e^(−9t) x(0) = x′(0) = x^(′′) (0) = 0 Use Laplace Transformation to solve it .

$$\frac{{d}^{\mathrm{3}} {x}}{{dt}^{\mathrm{3}} }\:+\:\mathrm{27}\:\frac{{d}^{\mathrm{2}} {x}}{{dt}^{\mathrm{2}} }\:+\:\mathrm{243}\:\frac{{dx}}{{dt}}\:+\:\mathrm{729}{x}\:=\:{t}\centerdot\:{e}^{−\mathrm{9}{t}} \\ $$$$\:\:\:\:\:\:{x}\left(\mathrm{0}\right)\:=\:{x}'\left(\mathrm{0}\right)\:=\:{x}^{''} \left(\mathrm{0}\right)\:=\:\mathrm{0} \\ $$$${Use}\:\:{Laplace}\:\:{Transformation}\:\:{to}\:\:{solve}\:\:{it}\:. \\ $$

Question Number 91813 Answers: 0 Comments: 3

lim_(x→1) ((1−x+ ln x)/(1−(√(2x−x^2 )))) ?

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{1}−{x}+\:\mathrm{ln}\:{x}}{\mathrm{1}−\sqrt{\mathrm{2}{x}−{x}^{\mathrm{2}} }}\:? \\ $$

Question Number 91812 Answers: 0 Comments: 2

Solve clairaut′s equation and find general and singular solution: (i) y=px+p^n (ii) (y+1)p−xp^2 +2=0

$$\:\mathrm{Solve}\:\mathrm{clairaut}'\mathrm{s}\:\mathrm{equation}\:\mathrm{and}\:\mathrm{find} \\ $$$$\:\mathrm{general}\:\mathrm{and}\:\mathrm{singular}\:\mathrm{solution}: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{y}=\mathrm{px}+\mathrm{p}^{\mathrm{n}} \\ $$$$\:\left(\mathrm{ii}\right)\:\left(\mathrm{y}+\mathrm{1}\right)\mathrm{p}−\mathrm{xp}^{\mathrm{2}} +\mathrm{2}=\mathrm{0} \\ $$$$ \\ $$$$ \\ $$

Question Number 92521 Answers: 0 Comments: 10

Question Number 92518 Answers: 1 Comments: 0

Question Number 92510 Answers: 1 Comments: 1

(1/(D^2 +2)) (sin 2x) ?

$$\frac{\mathrm{1}}{\mathrm{D}^{\mathrm{2}} +\mathrm{2}}\:\left(\mathrm{sin}\:\mathrm{2x}\right)\:?\: \\ $$

Question Number 92511 Answers: 0 Comments: 2

lim_(x→0) (((x)^(1/3) −(x)^(1/5) )/((x)^(1/3) −(x)^(1/4) ))

$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{x}}−\sqrt[{\mathrm{5}}]{\mathrm{x}}}{\sqrt[{\mathrm{3}}]{\mathrm{x}}−\sqrt[{\mathrm{4}}]{\mathrm{x}}} \\ $$

Question Number 91796 Answers: 1 Comments: 1

Total sum of this below infinite series : 1). (1/(1×2))+(1/(2×3))+(1/(3×4))+...(1/(n(n+1)))=... 2). 0.6+0.06+0.006+...(6/(10^n ))=...

$$\mathrm{Total}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{this}\:\mathrm{below}\:\mathrm{infinite}\:\mathrm{series}\:: \\ $$$$\left.\mathrm{1}\right).\:\:\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}×\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}}+...\frac{\mathrm{1}}{\mathrm{n}\left(\mathrm{n}+\mathrm{1}\right)}=... \\ $$$$\left.\mathrm{2}\right).\:\:\mathrm{0}.\mathrm{6}+\mathrm{0}.\mathrm{06}+\mathrm{0}.\mathrm{006}+...\frac{\mathrm{6}}{\mathrm{10}^{\mathrm{n}} }=... \\ $$

Question Number 91786 Answers: 0 Comments: 7

repost question from mr jagoll { ((2+6y = (x/y)−(√(x−2y)))),(((√(x+(√(x−2y)))) = x+3y−2 )) :}

$${repost}\:{question}\:{from} \\ $$$${mr}\:{jagoll} \\ $$$$\begin{cases}{\mathrm{2}+\mathrm{6}{y}\:=\:\frac{{x}}{{y}}−\sqrt{{x}−\mathrm{2}{y}}}\\{\sqrt{{x}+\sqrt{{x}−\mathrm{2}{y}}}\:=\:{x}+\mathrm{3}{y}−\mathrm{2}\:}\end{cases} \\ $$

Question Number 91785 Answers: 0 Comments: 5

given these bellow sequenses . find fifth term 1). (1/5), (1/4) , (3/(11)), (2/7),... 2). (3/5), ((−9)/(11)) , ((−25)/(19)), ((57)/(35)),... 3). (1/6), (7/(11)) , ((13)/(16)), ((19)/(21)),... 4). 4,− (2/3) , −(4/(13)),− (1/5),... 5). 2, 9 , 28 , 65,...

$$\mathrm{given}\:\:\mathrm{these}\:\mathrm{bellow}\:\mathrm{sequenses}\:.\: \\ $$$$\mathrm{find}\:\mathrm{fifth}\:\mathrm{term} \\ $$$$ \\ $$$$\left.\mathrm{1}\right).\:\:\frac{\mathrm{1}}{\mathrm{5}},\:\frac{\mathrm{1}}{\mathrm{4}}\:,\:\frac{\mathrm{3}}{\mathrm{11}},\:\frac{\mathrm{2}}{\mathrm{7}},... \\ $$$$\left.\mathrm{2}\right).\:\:\frac{\mathrm{3}}{\mathrm{5}},\:\frac{−\mathrm{9}}{\mathrm{11}}\:,\:\frac{−\mathrm{25}}{\mathrm{19}},\:\frac{\mathrm{57}}{\mathrm{35}},... \\ $$$$\left.\mathrm{3}\right).\:\:\:\frac{\mathrm{1}}{\mathrm{6}},\:\frac{\mathrm{7}}{\mathrm{11}}\:,\:\frac{\mathrm{13}}{\mathrm{16}},\:\frac{\mathrm{19}}{\mathrm{21}},... \\ $$$$\left.\mathrm{4}\right).\:\:\:\mathrm{4},−\:\frac{\mathrm{2}}{\mathrm{3}}\:,\:−\frac{\mathrm{4}}{\mathrm{13}},−\:\frac{\mathrm{1}}{\mathrm{5}},... \\ $$$$\left.\mathrm{5}\right).\:\:\mathrm{2},\:\mathrm{9}\:,\:\mathrm{28}\:,\:\mathrm{65},... \\ $$

Question Number 91783 Answers: 0 Comments: 1

1). (1/2), (2/3), (3/4) , (4/5), ..., .... 2). 4,6,10,18,34,...,.... 3). 5,7,11,19,35,...,.... 4). 4,6,10,18,34,...,.... 5). 4,11,30,85,248,...,...

$$\left.\mathrm{1}\right).\:\:\frac{\mathrm{1}}{\mathrm{2}},\:\frac{\mathrm{2}}{\mathrm{3}},\:\frac{\mathrm{3}}{\mathrm{4}}\:,\:\frac{\mathrm{4}}{\mathrm{5}},\:...,\:.... \\ $$$$\left.\mathrm{2}\right).\:\:\mathrm{4},\mathrm{6},\mathrm{10},\mathrm{18},\mathrm{34},...,.... \\ $$$$\left.\mathrm{3}\right).\:\:\mathrm{5},\mathrm{7},\mathrm{11},\mathrm{19},\mathrm{35},...,.... \\ $$$$\left.\mathrm{4}\right).\:\:\mathrm{4},\mathrm{6},\mathrm{10},\mathrm{18},\mathrm{34},...,.... \\ $$$$\left.\mathrm{5}\right).\:\:\mathrm{4},\mathrm{11},\mathrm{30},\mathrm{85},\mathrm{248},...,... \\ $$

Question Number 91774 Answers: 0 Comments: 0

∫_0 ^∞ ((sin^k (x))/x^k )dx for any k>0

$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}\:^{{k}} \left({x}\right)}{{x}^{{k}} }{dx}\:{for}\:{any}\:{k}>\mathrm{0} \\ $$

Question Number 91771 Answers: 0 Comments: 1

∫_0 ^∞ ((sin^3 (x))/x^2 )dx

$$\int_{\mathrm{0}} ^{\infty} \frac{{sin}^{\mathrm{3}} \left({x}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 91770 Answers: 1 Comments: 2

y′′+3y=x^3 +3x