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undetermined
undeˈtermined, ppl. a. [un-1 8 and 5 b.] 1. Not authoritatively decided or settled; not brought to an end by decision.1442 in Proc. King's Council Irel. (Rolls) 275 Many grete tresons..stonde yet vndetermyned. a 1513 Fabyan Chron. vii. ccxxviii. 257 The pope gaue suche a defuse sentence in this mate... Oxford English Dictionary
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Method of undetermined coefficients
In mathematics, the method of undetermined coefficients is an approach to finding a particular solution to certain nonhomogeneous ordinary differential Undetermined coefficients is not as general a method as variation of parameters, since it only works for differential equations that follow certain forms wikipedia.org
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Find particular solution by method of undetermined coefficients
Mar 10, 2023I am trying to find the general form of a particular solution suggested by the method of undetermined coefficients for the DE: $$ (D^2 + 6D + 10)^2 y = x^3e^{-3x}\sin(x) $$ where $ D = \frac{d}{dx} $ I have solved the characteristic equation of the left side and found the roots to be
math.stackexchange.com 0.0 0.90000004 0.0
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Differential Equations - Undetermined Coefficients - Pauls Online Math ...
Nov 16, 2022Section 3.9 : Undetermined Coefficients. In this section we will take a look at the first method that can be used to find a particular solution to a nonhomogeneous differential equation. y′′ +p(t)y′ +q(t)y = g(t) y ″ + p ( t) y ′ + q ( t) y = g ( t) One of the main advantages of this method is that it reduces the problem down to an ...
tutorial.math.lamar.edu 0.0 0.6 0.0
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Undetermined vs. Undefined This often comes up in precalculus and calculus, that is sometimes an expression will be said to undefined while at other times undetermined. What is the fundamental difference between the t...
Some say that the value of the _fraction_ $0/0$ (no reference to limits) is undetermined, but this has no real usefulness.
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Embolic stroke of undetermined source
Embolic stroke of undetermined source (ESUS) is an embolic stroke, a type of ischemic stroke, with an unknown origin, defined as a non-lacunar brain infarct wikipedia.org
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I heard that $0/0$ is undetermined, why is $\infty/\infty$ also undetermined? I heard that $0/0$ is undetermined, but why is $\infty/\infty$ also undetermined? Also what is $\lim\limits_{x \to \infty} \frac{x}{x}$ and...
A short and non rigorous explanation: in a fraction $\dfrac{P(x)}{Q(x)}$ (assume that both $P(x)$ and $Q(x)$ are positive) it may happen that $P(x)$ goes to infinity "faster", "slower" or "as fast as" $Q(x)$. Depending on these speeds the fraction tends to infinity, zero or a constant, or it may hap...
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Monoclonal gammopathy of undetermined significance
Monoclonal gammopathy of undetermined significance (MGUS) is a plasma cell dyscrasia in which plasma cells or other types of antibody-producing cells secrete wikipedia.org
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undetermined coefficients in DE given y"+4y'=16x find a general solution through undetermined coefficients. I have found yc to be yc = c1 + c2e^(-x) and I have chosen yp to be yp = ax^2 + bx Just wondering if thi...
Your complementary functions contains a constant $c_1$, so you are correct in multiply the "usual/default" particular integral $y_{p_o} = ax + b$ by $x$ to get $y_p = ax^2 + bx$.
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Theory of the Undetermined Status of Taiwan
The Theory of the Undetermined Status of Taiwan (), also called the Theory of the Undetermined Sovereignty of Taiwan (), is one of the theories which describe The Theory of the Undetermined Status of Taiwan is supported by some politicians and jurists to this day. wikipedia.org
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Concerning undetermined coefficients method if $f(x)=\sin(2x)\sin(x)$ for the non homogeneous higher order ODE $$y''-3y'+2y=\sin(2x)\sin(x) $$ if we want to solve using undetermined coefficients , can we assume that t...
No, you can not assume that you get such a factorization. However, you can use trigonometric identities to get $$ \sin(x)\sin(2x)=\frac12(\cos(x)-\cos(3x)) $$ and compute the particular solutions for each term separately. * * * Your friendly helper WolframAlpha gives the solution as follows, which o...
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The method of undetermined coeficients for a non-homogenous linear ODE with a rational RHS Consider the equation $$\ddot x-5\dot x+4x=\frac{9e^t}{1+e^{-3t}}$$ The characteristic roots are one and four. The solution to...
Set $$x(t) = C_1(t) x_1(t),$$ where $x_i(t) = e^{s_i t}$, $s_i = \\{1,4\\}$ (you can chose any of the roots). Differentiate now to obtain $x'$ and $x''$ and substitute back into the original ODE. Take into account that $x_1'' - 5x_1'+ 4x_1 = 0$ and solve for $C_1$. Can you take it from here? Let us ...
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Method of Undetermined Coefficients So the question asks me to use a method of undetermined coefficients to compute $a_1,a_2$ and $a_3$ such that $Df(x,h) = a_1f(x+h)+a_2f(x+2h)+a_3f(x+4h)$ is a second order accura...
Expand in a Taylor's series: $$a_1f(x+h) = a_1f(x) + a_1h Df(x) + a_1\frac{h^2}{2} D^2 f(x) + \cdots$$ $$a_2f(x+2h) = a_2f(x) + 2a_2h Df(x) + 2a_2h^2 D^2 f(x) + \cdots$$ $$a_3f(x+4h) = a_3f(x) + 4a_3h Df(x) + 8a_3h^2 D^2 f(x) + \cdots$$ Then we need the coefficients on the zeroth derivative to vanis...
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Undetermined game of length $\omega_1+\omega$, without choice On the following page, Taranovsky is talking about his "Determinacy Maximum" axiom: < He also justifies the choice of the name, by pointing out that many ...
Either X does not have a perfect subset (so the perfect subset game corresponding to X is undetermined), or a well-ordering of ℝ (and hence an undetermined The following game of length $ω_1$ is undetermined.
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DE undetermined coefficients De problem $$x'' + 196x = 40\sin (14t)$$ I have the general solution, I'm just struggling with the algebra with the undetermined coefficient. I set my guess as: $At\cos (14t) + Bt\sin (14...
Your choice for a particular solution is correct. We have: $$x_p'' = t (-196 a \cos (14 t)-196 b \sin (14 t))-28 a \sin (14 t)+28 b \cos (14 t)$$ So, $$x_p'' + 196 x_p = 28 (b \cos (14 t)-a \sin (14 t)) = 40 \sin(14 t)$$ Equating terms, we get: $$a = -\dfrac{10}{7}, b = 0$$ This gives a final soluti...
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