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Question Number 184311    Answers: 1   Comments: 0

Question Number 184307    Answers: 1   Comments: 0

Show that the boundary−value problem y′′+λy=0 y(0)=0, y(L)=0 has only the trival solution y=0 for the cases λ=0 and λ<0. let L be a non−zero real number. ?

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{boundary}−\mathrm{value} \\ $$$$\mathrm{problem}\:\mathrm{y}''+\lambda\mathrm{y}=\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{0}, \\ $$$$\mathrm{y}\left(\mathrm{L}\right)=\mathrm{0}\:\mathrm{has}\:\mathrm{only}\:\mathrm{the}\:\mathrm{trival}\:\mathrm{solution} \\ $$$$\mathrm{y}=\mathrm{0}\:\mathrm{for}\:\mathrm{the}\:\mathrm{cases}\:\lambda=\mathrm{0}\:\mathrm{and}\:\lambda<\mathrm{0}. \\ $$$$\mathrm{let}\:\mathrm{L}\:\mathrm{be}\:\mathrm{a}\:\mathrm{non}−\mathrm{zero}\:\mathrm{real}\:\mathrm{number}. \\ $$$$ \\ $$$$ \\ $$$$? \\ $$

Question Number 184306    Answers: 1   Comments: 0

Consider the boundary value problem y^(′′) −2y′+2y=0, y(a)=c ,y(b)=d. 1) If this problem has a unique solution, how are a and b related? 2) If this problem has no solution, how are a,b,c and d related? Help!

$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{boundary}\:\mathrm{value}\: \\ $$$$\mathrm{problem}\:\mathrm{y}^{''} −\mathrm{2y}'+\mathrm{2y}=\mathrm{0},\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{a}\right)=\mathrm{c} \\ $$$$,\mathrm{y}\left(\mathrm{b}\right)=\mathrm{d}. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{If}\:\mathrm{this}\:\mathrm{problem}\:\mathrm{has}\:\mathrm{a}\:\mathrm{unique} \\ $$$$\mathrm{solution},\:\mathrm{how}\:\mathrm{are}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{related}? \\ $$$$\left.\mathrm{2}\right)\:\mathrm{If}\:\mathrm{this}\:\mathrm{problem}\:\mathrm{has}\:\mathrm{no}\:\mathrm{solution}, \\ $$$$\mathrm{how}\:\mathrm{are}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{and}\:\mathrm{d}\:\mathrm{related}? \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184264    Answers: 1   Comments: 0

Question Number 184218    Answers: 1   Comments: 0

Question Number 184188    Answers: 1   Comments: 0

Differentiate, y = x^(x−1) hi

$$\mathrm{Differentiate},\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{x}−\mathrm{1}} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{hi} \\ $$

Question Number 184187    Answers: 1   Comments: 0

Differentiate, y=e^x + x^x M.m

$$\mathrm{Differentiate},\:\mathrm{y}=\mathrm{e}^{\mathrm{x}} \:+\:\mathrm{x}^{\mathrm{x}} \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 184185    Answers: 1   Comments: 0

Differentiate, y=(log_e x)^x M.m

$$\mathrm{Differentiate},\:\mathrm{y}=\left(\mathrm{log}_{\mathrm{e}} \mathrm{x}\right)^{\mathrm{x}} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 184184    Answers: 1   Comments: 0

y=(sinx)^x Differentiate

$$\mathrm{y}=\left(\mathrm{sinx}\right)^{\mathrm{x}} \\ $$$$ \\ $$$$\mathrm{Differentiate} \\ $$

Question Number 184126    Answers: 1   Comments: 0

Question Number 184125    Answers: 0   Comments: 0

Question Number 184048    Answers: 5   Comments: 0

{ ((u_0 = 2)),((u_(n+1) = ((2u_n −1)/u_n ))) :} Find u_n .

$$\:\:\begin{cases}{{u}_{\mathrm{0}} \:=\:\mathrm{2}}\\{{u}_{{n}+\mathrm{1}} \:=\:\frac{\mathrm{2}{u}_{{n}} \:−\mathrm{1}}{{u}_{{n}} }}\end{cases} \\ $$$$\:\:\:{Find}\:{u}_{{n}} . \\ $$

Question Number 184030    Answers: 1   Comments: 0

How many words can be made from 5 letters if (a) all letters are different (b) 2 letters are identical (c) all letters are different but 2 partucular letters cannot be adjacent. M.m

$$\mathrm{How}\:\mathrm{many}\:\mathrm{words}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made}\: \\ $$$$\mathrm{from}\:\mathrm{5}\:\mathrm{letters}\:\mathrm{if} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{all}\:\mathrm{letters}\:\mathrm{are}\:\mathrm{different} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{2}\:\mathrm{letters}\:\mathrm{are}\:\mathrm{identical} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{all}\:\mathrm{letters}\:\mathrm{are}\:\mathrm{different}\:\mathrm{but}\:\mathrm{2} \\ $$$$\mathrm{partucular}\:\mathrm{letters}\:\mathrm{cannot}\:\mathrm{be} \\ $$$$\mathrm{adjacent}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 184028    Answers: 0   Comments: 0

H^(A^P P) Y Y_(E_A R) ! ⌊e⌋⌊i-i⌋⌊e⌋⌊𝛑⌋^(−)

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{H}}^{\boldsymbol{\mathrm{A}}^{\boldsymbol{\mathrm{P}}} \boldsymbol{\mathrm{P}}} \boldsymbol{\mathrm{Y}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Y}}_{\boldsymbol{\mathrm{E}}_{\boldsymbol{\mathrm{A}}} \boldsymbol{\mathrm{R}}} \:! \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\overline {\lfloor\boldsymbol{\mathrm{e}}\rfloor\lfloor\boldsymbol{\mathrm{i}}-\boldsymbol{\mathrm{i}}\rfloor\lfloor\boldsymbol{\mathrm{e}}\rfloor\lfloor\boldsymbol{\pi}\rfloor}\:\: \\ $$

Question Number 184010    Answers: 0   Comments: 3

determinant ((( determinant (((2023))) )))_( is^ _(a number_(which is divisible_(by_(•_• ) ) ) ) ) (i)its sum of digits & (ii)its sum of squares of digits

$$\:\:\:\:\:\:\:\:\:\:\underset{\:\underset{\underset{\underset{\underset{\underset{\bullet} {\bullet}} {\boldsymbol{\mathrm{by}}}} {\boldsymbol{\mathrm{which}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{divisible}}}} {\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{number}}}} {\boldsymbol{\mathrm{is}}^{\:} }} {\begin{array}{|c|}{\:\begin{array}{|c|}{\mathrm{2023}}\\\hline\end{array}\:}\\\hline\end{array}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\boldsymbol{\mathrm{i}}\right)\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{digits}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\& \\ $$$$\:\:\:\:\:\:\:\left(\boldsymbol{\mathrm{ii}}\right)\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{squares}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{digits}} \\ $$

Question Number 183913    Answers: 0   Comments: 0

Question Number 183737    Answers: 2   Comments: 0

Question Number 183687    Answers: 3   Comments: 0

∫(1/(lnx))dx Help out

$$\int\frac{\mathrm{1}}{\mathrm{lnx}}\mathrm{dx} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}\:\mathrm{out} \\ $$

Question Number 183667    Answers: 0   Comments: 8

If w is one of the complex cube roots of unity, show that (a+wb+w^2 c)(a+w^2 b+wc) is equal to (α^2 +b^2 +c^2 −ab−bc−cα). Kindly help me out, Thank you.

$$\mathrm{If}\:\mathrm{w}\:\mathrm{is}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{cube}\: \\ $$$$\mathrm{roots}\:\mathrm{of}\:\mathrm{unity},\:\mathrm{show}\:\mathrm{that} \\ $$$$\left(\mathrm{a}+\mathrm{wb}+\mathrm{w}^{\mathrm{2}} \mathrm{c}\right)\left(\mathrm{a}+\mathrm{w}^{\mathrm{2}} \mathrm{b}+\mathrm{wc}\right)\:\mathrm{is}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\left(\alpha^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} −\mathrm{ab}−\mathrm{bc}−\mathrm{c}\alpha\right). \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Kindly}\:\mathrm{help}\:\mathrm{me}\:\mathrm{out},\:\mathrm{Thank}\:\mathrm{you}. \\ $$

Question Number 183600    Answers: 1   Comments: 3

y′^(′′) + 8y′^(′′) +12y′ = 0 Solve with better explanation

$$\mathrm{y}'^{''} \:+\:\mathrm{8y}'^{''} \:+\mathrm{12y}'\:=\:\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Solve}\:\mathrm{with}\:\mathrm{better}\:\mathrm{explanation} \\ $$

Question Number 183465    Answers: 1   Comments: 0

Find the least value of (1−2x)(1−x). M.m

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\left(\mathrm{1}−\mathrm{2x}\right)\left(\mathrm{1}−\mathrm{x}\right). \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 183464    Answers: 2   Comments: 0

Find the Maximum value of 3x(4−x) M.m

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{Maximum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{3x}\left(\mathrm{4}−\mathrm{x}\right) \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 183211    Answers: 1   Comments: 0

y^((iv)) +16y^((iii)) +9y^((ii)) +256y^((i)) +256y=0 M.m

$$\mathrm{y}^{\left(\mathrm{iv}\right)} +\mathrm{16y}^{\left(\mathrm{iii}\right)} +\mathrm{9y}^{\left(\mathrm{ii}\right)} +\mathrm{256y}^{\left(\mathrm{i}\right)} +\mathrm{256y}=\mathrm{0} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 183210    Answers: 1   Comments: 0

(d^3 y/dx^3 )+4(d^2 y/dx^2 )+(dy/dx)−6y=0 M.m

$$\frac{\mathrm{d}^{\mathrm{3}} \mathrm{y}}{\mathrm{dx}^{\mathrm{3}} }+\mathrm{4}\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }+\frac{\mathrm{dy}}{\mathrm{dx}}−\mathrm{6y}=\mathrm{0} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 183209    Answers: 1   Comments: 0

Solve the Differential equation below (d^3 y/dx^3 )+8(d^2 y/dx^2 )+12(dy/dx)=0 M.m

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{Differential}\:\mathrm{equation}\:\mathrm{below} \\ $$$$\frac{\mathrm{d}^{\mathrm{3}} \mathrm{y}}{\mathrm{dx}^{\mathrm{3}} }+\mathrm{8}\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }+\mathrm{12}\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{0} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 183117    Answers: 2   Comments: 0

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