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Question Number 211531 Answers: 1 Comments: 0

∫_0 ^∞ (x^2 /(sinh(x)^2 ))dx.

$\int_{0}^{\infty} \frac{x^{2}}{\sinh {(x)}^{2}} d x .$

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does anyone know if charpit′s method for solving PDE can be used to solve second order pde? Also is it possible to reduce second order PDE to first order?

$does anyone know if {charpit}^{'} s method for solving$ $PDE can be used to solve second order pde ?$ $Also is it possible to reduce second order PDE to first order ?$

Question Number 210912 Answers: 2 Comments: 0

A uniform stick AB of length L and mass M is balanced horizontally on a knife edge 10.0cm from A when an object of mass 400g is suspended at A. When the knife edge is moved 5cm further, the object has to be moved to a point 9.00cm from A for the stick to balance. Represent the balance system with a suitable diagram, determine the mass and Length of the stick

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MATH−WHIZZKID using kamke find the genral solution for the differential equation 1. x^2 y′′+x^2 y′−2y=0 −−−−−−−−− solve this using forbenius mtd 1.x^2 y′′+(x^3 −3x)y′+(4−2x)y=0 −−−−−−−− solve the differential eqn by power series 1. y′′−2xy′+2py=0 −−−−−−−−− use perseval′s theorem to ∫_0 ^∞ ((cos^2 (𝛂(𝛑/2)))/((1−𝛂^2 )^2 ))dx. −−−−−−−−−− evaluate this integral by contour integration 1. ∫_0 ^∞ ((cos^2 (𝛂(𝛑/2)))/((1−𝛂^2 )^2 ))dx. −−−−−−−−− ∮_c ((1+e^(i𝛑z) )/((z−1)^2 (z+1)^2 ))dz c−upper half plane klipto−quanta⊎

$MATH - WHIZZKID$ $using kamke find the genral$ $solution for the differential equation$ $1 . x^{2} y^{″} + x^{2} y^{'} - 2 y = 0$ $- - - - - - - - -$ $solve this using forbenius mtd$ $1 . x^{2} y^{″} + (x^{3} - 3 x) y^{'} + (4 - 2 x) y = 0$ $- - - - - - - -$ $solve the differential eqn by power series$ $1 . y^{″} - 2 {xy}^{'} + 2 py = 0$ $- - - - - - - - -$ $use {perseval}^{'} s theorem to$ $\int_{0}^{\infty} \frac{\cos^{2} (α \frac{π}{2})}{{(1 - α^{2})}^{2}} dx .$ $- - - - - - - - - -$ $evaluate this integral by contour integration$ $1 . \int_{0}^{\infty} \frac{\cos^{2} (α \frac{π}{2})}{{(1 - α^{2})}^{2}} dx .$ $- - - - - - - - -$ $\oint_{c} \frac{1 + e^{i π z}}{{(z - 1)}^{2} {(z + 1)}^{2}} dz$ $c - upper half plane$ $klipto - quanta ⨄$

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Question Number 209631 Answers: 0 Comments: 0

Let u_n be a set satisfying u_1 =1 & u_(n+1) =u_n +((ln n)/u_n ) , ∀ n ≥1 1. Prove that u_(2023) >(√(2023.ln 2023)). 2. Find: lim_(n→∞) ((u_n .ln n)/n).

$Let u_{n} be a set satisfying u_{1} = 1 & u_{n + 1} = u_{n} + \frac{\ln n}{u_{n}}, \forall n ⩾ 1$ $1 . Prove that u_{2023} > \sqrt{2023 . \ln 2023} .$ $2 . Find : \lim_{n \to \infty} \frac{u_{n} . \ln n}{n} .$