Advanced Math Archive: Questions from March 23, 2023
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1. Let \[ G(x, y)=\left[\ln |x-y|-\ln \left(\left|\frac{x}{|x|}-\right| x|y|\right)\right] \] Verify that it satisfies \[ \Delta G(x, y)=0, \quad \forall x, y \in B_{1}(0), x \neq y \] and \[ G(x, y)=2 answers -
(4) Find the general solution for each differential equation and then solve he initial value problems (a) \( 3 y^{\prime \prime}+y^{\prime}=0: y(0)=6, y^{\prime}(0)=2 \) (b) \( 2 y^{\prime \prime}+182 answers -
Evaluate the double integral. \[ \iint_{D} 9 x d A, \quad D=\{(x, y) \mid 0 \leq x \leq \pi, 0 \leq y \leq \sin (x)\} \]2 answers -
Draw the original flowchart given that the following formulation will converts to a series of streams “A” (t=3-6). A= [(-800-40(A/G,i,4)](P/A,i,4)(F/P,i,4)(A/P,i,4) + [1,000 + 5,300(P/F,i,3)](F/P,
Dibuje el diagrama de flujo original dado que la siguiente formulación lo convierte a una serie de flujos " \( \mathrm{A} \) " \( (\mathrm{t}=3-6) \). \[ \begin{array}{l} \mathrm{A}=[(-800-40(\mathrm0 answers -
first order linear equations: (1) \( \sin y \frac{d x}{d y}+x \sec y=\cos ^{2} y \) (2) \( x\left(y^{\prime}-x \cos x\right)=y \) (3) \( y^{\prime}+2 y \tan x=\sin x \) (4) \( y^{\prime}+y=e^{x} \) (52 answers -
Homogenous equations: \( \left\{\begin{array}{l}\left(y+\sqrt{x^{2}+y^{2}}\right) d x-x d y=0 \\ y(1)=0\end{array}\right. \) 1) 2) \( y^{\prime}=\frac{2 x y}{x^{2}-y^{2}} \) 3) \( y^{\prime}=\frac{(x-2 answers -
2 answers
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#6 please im getting stuck
In Problems \( 1-8 \), find a general solution to the differential equation using the method of variation of parameters. 1. \( y^{\prime \prime}+4 y=\tan 2 t \) 2. \( y^{\prime \prime}+y=\sec t \) 3.2 answers -
7. Solve \( y^{\prime \prime}-2 y^{\prime}+y=\frac{e^{x}}{1+x^{2}} \) using variation of parameters.2 answers -
Solve The following differential equations Q1) \( y^{\prime} \sin (2 \pi x)=\pi y \sin (2 \pi x) \) Q2) \( (2 x y-\tan y) d x+\left(x^{2}-x \sec ^{2} y\right) d y=0 \) Q3) \( (x+2) \sin y d x+x \cos y2 answers -
Suponer que la población de una ciudad satisface la hipótesis logística: "La razón de cambio de la población en cualquier momento es proporcional al producto de la población en ese momento y la2 answers -
number 4,6,9,11,12
In Problems 1-14 find the general solution of the given second-order differential equation. 1. \( 4 y^{\prime \prime}+y^{\prime}=0 \) 2. \( y^{\prime \prime}-36 y=0 \) 3. \( y^{\prime \prime}-y^{\prim2 answers -
INSTRUCTIONS: Write the linear functions represented in the following graph.
1. Escribe las funciones lineales \( f(x) \) y \( g(x) \) representadas en la siguiente gráfica. (Valor 6 puntos). Ecuaciones: \( f(x)= \) \[ g(x)= \]2 answers -
2, 12, 13
In Problems 1-26 solve the given differential equation by undeter- 9. \( y^{\prime \prime}-y^{\prime}=-3 \) nined coefficients. 10. \( y^{\prime \prime}+2 y^{\prime}=2 x+5-e^{-2 x} \) 1. \( y^{\prime2 answers -
28, 31 differential equations
In Problems \( 27-36 \) solve the given initial-value problem. 27. \( y^{\prime \prime}+4 y=-2, \quad y(\pi / 8)=\frac{1}{2}, y^{\prime}(\pi / 8)=2 \) 28. \( 2 y^{\prime \prime}+3 y^{\prime}-2 y=14 x^2 answers -
1.-Dada la siguiente tabla encuentra el valor para \( x_{k}=0.6 \) usando la fórmula avanzada de interpolación de Newton (redondea a 4 decimales). 2.- Completa la siguiente tabla, encuentra el valo2 answers