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Question Number 201582 Answers: 0 Comments: 0

Solve.... y′′(t)−sin(t)y(t)=0 , y^((2)) (0)=0 , y^((1)) (0)=−1 , y(0)=0 L{y′′(t)−sin(t)y(t)}=0 s^2 F(s)−sy(0)−y′(0)−L{sin(t)y(t)}=0 Holy...×uck I already know y′′(t)−ty(t)=0 solution C_1 Ai(t)+C_2 Bi(t) But I Can′t Solve y′′(t)−sin(t)y(t)=0....

$$\mathrm{Solve}.... \\ $$$${y}''\left({t}\right)−\mathrm{sin}\left({t}\right){y}\left({t}\right)=\mathrm{0}\:,\: \\ $$$${y}^{\left(\mathrm{2}\right)} \left(\mathrm{0}\right)=\mathrm{0}\:,\:{y}^{\left(\mathrm{1}\right)} \left(\mathrm{0}\right)=−\mathrm{1}\:,\:{y}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\boldsymbol{\mathcal{L}}\left\{{y}''\left({t}\right)−\mathrm{sin}\left({t}\right){y}\left({t}\right)\right\}=\mathrm{0} \\ $$$${s}^{\mathrm{2}} \boldsymbol{\mathrm{F}}\left({s}\right)−{sy}\left(\mathrm{0}\right)−{y}'\left(\mathrm{0}\right)−\boldsymbol{\mathcal{L}}\left\{\mathrm{sin}\left({t}\right){y}\left({t}\right)\right\}=\mathrm{0} \\ $$$$\mathrm{Holy}...×\mathrm{uck} \\ $$$$\mathrm{I}\:\mathrm{already}\:\mathrm{know}\:{y}''\left({t}\right)−{ty}\left({t}\right)=\mathrm{0}\:\:\:\mathrm{solution} \\ $$$$\mathrm{C}_{\mathrm{1}} \mathrm{Ai}\left({t}\right)+{C}_{\mathrm{2}} \mathrm{Bi}\left({t}\right) \\ $$$$\mathrm{But}\:\mathrm{I}\:\mathrm{Can}'\mathrm{t}\:\mathrm{Solve}\:{y}''\left({t}\right)−\mathrm{sin}\left({t}\right){y}\left({t}\right)=\mathrm{0}....\: \\ $$

Question Number 201581 Answers: 1 Comments: 0

Question Number 201573 Answers: 1 Comments: 0

Question Number 201562 Answers: 3 Comments: 0

Question Number 201561 Answers: 1 Comments: 0

Question Number 201553 Answers: 3 Comments: 0

Question Number 201548 Answers: 1 Comments: 0

Question Number 201547 Answers: 1 Comments: 0

Question Number 201546 Answers: 2 Comments: 4

∫Sin(Inx)dx

$$\:\:\:\int\boldsymbol{{Sin}}\left(\boldsymbol{{Inx}}\right)\boldsymbol{{dx}} \\ $$

Question Number 201545 Answers: 0 Comments: 0

Question Number 201544 Answers: 2 Comments: 0

Question Number 201533 Answers: 2 Comments: 0

Un = ln (cos (1/2^n ) ) show that Un ≤0

$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{Un}\:=\:{ln}\:\left({cos}\:\frac{\mathrm{1}}{\mathrm{2}^{{n}} }\:\right) \\ $$$$\:\:\:\:{show}\:\:{that}\:{Un}\:\leqslant\mathrm{0} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 201534 Answers: 0 Comments: 1

let f(x)=tanx find f^((n)) (x) with n integr natural

$${let}\:{f}\left({x}\right)={tanx} \\ $$$${find}\:{f}^{\left({n}\right)} \left({x}\right)\:{with}\:{n}\:{integr} \\ $$$${natural} \\ $$

Question Number 201527 Answers: 1 Comments: 0

Question Number 201526 Answers: 1 Comments: 0

Question Number 201519 Answers: 3 Comments: 0

Question Number 201517 Answers: 1 Comments: 0

Question Number 201516 Answers: 1 Comments: 0

Question Number 201515 Answers: 1 Comments: 0

Question Number 201555 Answers: 1 Comments: 0

Question Number 201557 Answers: 2 Comments: 0

5 ∙ 555...5_( 50) find the sum of the digits of the product.

$$\mathrm{5}\:\centerdot\:\underset{\:\mathrm{50}} {\underbrace{\mathrm{555}...\mathrm{5}}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{product}. \\ $$

Question Number 201510 Answers: 1 Comments: 0

Question Number 201509 Answers: 1 Comments: 0

Question Number 201502 Answers: 0 Comments: 3

A generation is about one-third of a lifetime.Approximately about how many generations have passed since the year 0AD?

$${A}\:{generation}\:{is}\:{about}\:{one}-{third}\:{of}\:{a} \\ $$$${lifetime}.{Approximately}\:{about}\:{how} \\ $$$${many}\:{generations}\:{have}\:{passed}\:{since} \\ $$$${the}\:{year}\:\mathrm{0}{AD}? \\ $$

Question Number 201514 Answers: 0 Comments: 0

Question Number 201495 Answers: 1 Comments: 1

(Un)_(n≥1 ;) (1/(nC_(2n) ^n )) study convergence

$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\left({Un}\right)_{{n}\geqslant\mathrm{1}\:;} \:\:\:\:\frac{\mathrm{1}}{{nC}_{\mathrm{2}{n}} ^{{n}} \:} \\ $$$$ \\ $$$$\:\:\:\:{study}\:\:{convergence} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

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