Advanced Math Archive: Questions from December 06, 2022
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Analyze if the function satisfies the Cauchy-Riemann equations at (0,0)
19) Onalizar si la función satifface las ecuaciones de Cauchy-ORiemann en \( (0,0) \) : \[ f(z)=\frac{x^{3}-3 x y^{2}}{x^{2}+y^{2}}-\frac{i y}{x^{2}+y^{2}} \]2 answers -
Find the solution of the following Differential Equation: y''-9y=(9x/e^(3x)) Pleass provide clear process and answers ! Thanksss
3. [16 pts.] Halla la solución de las siguientes ecuaciones diferenciales: \( \therefore \cdot \quad \cdot \cdots \quad-\quad+v=e^{\prime \prime} \) b) \( y^{\prime \prime}-9 y=\frac{\ldots}{e^{3 x}}1 answer -
\( y^{\prime \prime}+0.5 y^{\prime}+25 y=\frac{4}{n^{2} \pi} \cos n t \quad(n=1,3,5, \cdots) \) \( y_{n}=A_{n} \cos n t+\beta n \sin n t, \quad y_{n}=? \)2 answers -
Verify that the differential equation (cos x + ln and ) dx +? # + e"@ dy = 0 is accurate, and " Then solve it.
3. [9 pts.] Verifica que la ecuación diferencial \( (\cos x+\ln y) d x+\left(\frac{x}{y}+e^{y}\right) d y=0 \) es exacta, y2 answers -
Solve the following Initial Value Problems x !" + y = 4x + 1; y(1) = 8.
[10 pts.] Resuelve los siguientes Problemas de Valor Inicial \( x \frac{d y}{d x}+y=4 x+1 ; y(1)=8 \)2 answers -
Consider the given vector field of the differential equation!" = 1 − xy, trace the curves ! # Solution that pass through the points y(−1) = 0 and y(0) = −4.
1. [5 pts.] Considera el campo vectorial dado de la ecuación diferencial \( \frac{d y}{d x}=1-x y \), traza las curvas de solución que pasan por los puntos \( y(-1)=0 \) y \( y(0)=-4 \).2 answers -
Which of the following differential equations represents a Mixing Model?
4. ¿Cuál de las siguientes ecuaciones diferenciales representa un Modelo de Mezclaje? a) \( \frac{d x}{d t}=-\alpha x \) b) \( \frac{d x}{d t}=20-\frac{1}{y} t \) c) \( \frac{d x}{d t}=\alpha(75-x)2 answers -
An integral factor of the linear differential equation x$y* + x(x + 1)y = e# is:
3. Un factor integrante de la ecuación diferencial lineal \( x^{2} y^{\prime}+x(x+1) y=e^{x} \) es: a) \( x \) b) \( e^{x} \) c) \( x e^{x} \) d) \( e^{\frac{x^{3}}{3}+\frac{x^{2}}{2}} \) e) Ninguna2 answers -
Find the solution to the initial value problem
2. [9 pts.| Halla la solución del Problema de Valor Inicial \( 4 y^{\prime \prime}+4 y^{\prime}+17 y=0 \); \( y(0)=-1, y^{\prime}(0)=2 \).2 answers -
2 answers
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Solve the IVP
\( \mathbf{y}^{\prime}=A \mathbf{y}, \quad \mathbf{y}(0)=\mathbf{y}_{0} \) \( A=\left(\begin{array}{cc}-1 & -4 \\ 1 & -1\end{array}\right), \quad y_{0}=\left(\begin{array}{c}-1 \\ 2\end{array}\right)2 answers -
wave equation
b) Resuelve la ecuación de onda con los siguientes valores de frontera \[ \frac{\partial^{2} u}{\partial x^{2}}=4 \frac{\partial^{2} u}{\partial y^{2}} \] \[ \begin{array}{l} u(0, t)=U(3, t)=0 \\ u(x1 answer -
verify divergence theorem
6. Sea el campo vectorial \[ F=\langle-y, x, z\rangle \] y el sólido \[ \left\{(x, y, z): x^{2}+y^{2} \leq 1 ;-2 \leq z \leq 3\right\} . \] Verificar el Teorema de la divergencia en este caso.1 answer -
(1 pt) Solve the following initial-boundary-value problem: \[ \begin{array}{r} u_{t}-\Delta u=0 \\ u(x, y, 0)=1 \\ u(0, y, t)=u(\pi, y, t)=0 \\ u(x, 0, t)=u(x, \pi, t)=0 \end{array} \] \[ u(x, y, t)=\2 answers -
2 answers
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please help with all of them
5. \( y^{\prime \prime}-y=1-H(t-2), y(0)=1, y^{\prime}(0)=0 \). 6. \( y^{\prime \prime}-2 y^{\prime}+y=t^{2} \delta(t-3), y(0)=0, y^{\prime}(0)=0 \). 7. \( y^{\prime}+\int_{0}^{t} f(u) \mathrm{d} u=\d2 answers -
Solve Laplace's equation, \( \frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}=0,02 answers -
1. (6 Pts.) Find all the possible values of \( \operatorname{Re}\left[2^{1+i}\right] \) and \( \log \left[2^{1+i}\right] \).2 answers -
Problema 2: Eddie Kelly está en la competencia para la reelección como alcalde de un pequeño condado de Alabama. Jéssica Martínez, la jefa de campaña de Kelly durante esta elección, está plane2 answers -
The point x=-1 is a singular point of the differential equation (cos(x))y''+y'+5y=0
3. El punto \( x=-1 \) es un punto singular de la ecuación diferencial \[ (\cos x) y^{\prime \prime}+y^{\prime}+5 y=0 \]2 answers -
Find the solution of rhe following system
2. [9 pts.] Halla la solución del sistema \[ \begin{aligned} D^{2} x-2\left(D^{2}+D\right) y & =\sin t \\ x+D y & =0 . \end{aligned} \]2 answers -
Find 2 solutions as Power Series around of x=0 for the differential equation (x-1)y''+y'=0
4. [10 pts.] Halla dos soluciones en series de potencias alrededor de \( x=0 \) para la ecuación diferencial \( (x-1) y^{\prime \prime}+y^{\prime}=0 \)2 answers -
\( \frac{10 \times 0,011}{(0,001)^{1 / 2}}=\frac{(2,5 y)^{5 / 3}}{(2,5+2 y)^{2 / 3}} \Rightarrow y=? \)0 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For Part of the surface \( x=z^{3} \), where \( 0 \leq x, y \leq 8^{-\frac{3}{2}} ; \quad f(x, y, z)=x \) \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ y=2-z^{2}, \quad 0 \leq x, z \leq 7 ; \quad f(x, y, z)=z \] \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ x^{2}+y^{2}=4, \quad 0 \leq z \leq 4 ; \quad f(x, y, z)=e^{-z} \] \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]2 answers -
If it is known that 2 and 2 - i are roots of the auxiliary equation of a differential equation, which has constant Cauchy-Euler coefficients, what would be the solution of said differential equation w
Si se sabe que 2 y \( 2-i \) son raíces de la ecuación auxiliar de una ecuación diferencial, que tiene coeficientes constantes Cauchy-Euler, ¿cuál sería la solución de dicha ecuación diferenci2 answers -
Please do question 4
4. \( y^{\prime}+2 y=e^{4 t}, y(0)=0 \). 5. \( y^{\prime \prime}-y=1-H(t-2), y(0)=1, y^{\prime}(0)=0 \). 6. \( y^{\prime \prime}-2 y^{\prime}+y=t^{2} \delta(t-3), y(0)=0, y^{\prime}(0)=0 \). 7. \( y^{2 answers -
2 answers
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3. Solve the system \[ \begin{array}{l} 2 x^{\prime}+y^{\prime}-4 x-y=e^{t} \\ x^{\prime}+3 x+y=0 \end{array} \]2 answers -
2 answers
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2 answers
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\( \frac{\sin (x+y)-\sin (x-y)}{\cos (x+y)+\cos (x-y)}=\tan y \) \( \frac{\sin 3 x+\sin 7 x}{\cos 3 x-\cos 7 x}=\cot 2 x \)2 answers -
9. Find all the asymptotes to the (i) \( y=e^{2 / x}-1 \) (iii) \( (y-2)\left(x^{2}-1\right)=5 \) (v) \( y=\frac{x-4}{x^{2}+4 x+3} \)2 answers