Advanced Math Archive: Questions from December 08, 2022
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2 answers
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\( f(x, y, z)=e^{\frac{y^{2}}{x^{2}+z^{2}}} \), compute \( \frac{\partial^{3} f}{\partial x \partial^{2} y} \)2 answers -
34. \( y^{\prime \prime}+2 y^{\prime}+y=0, y(-1)=0, y^{\prime}(0)=0 \) 38. \( 2 y^{\prime \prime}=3 y^{2}, y(0)=1, y^{\prime}(0)=1 \)2 answers -
2 answers
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Q.4 Solve the initial value problem \[ \begin{array}{r} y^{\prime \prime}+2 y^{\prime}+y=0 \\ y(0)=2, \quad y^{\prime}(0)=-1 \end{array} \]1 answer -
Let \[ \begin{array}{l} U=\{b, f, h, n, o, r, w, y\} \\ A=\{b, w, y\} \\ C=\{f, h, n, o, r\} \end{array} \] Find \( A \cup C^{\prime} \).2 answers -
Determina la ecuación a maximizar. Una companía produce dos equipos, El equipo A cuesta \( \$ 15 \) en producirse y el B cuesta \( \$ 90 \). La ganancia del equipo \( A \) es de \( \$ 90 y \) la del2 answers -
Utiliza el Método Simplex de Maximización. \[ \begin{array}{l} x+y \leq 14 \\ 11 x+88 y \leq 616 \\ x \geq 0, y \geq 0 \\ G=128 x+256 y \end{array} \] Completa la tabla de Simplex inicial. Pivote \(0 answers -
Let \( U=\{q, r, s, t, u, v, w, x, y, z\} ; A=\{q, s, u, w, y\} ; B=\{q, s, y, z\} ; \) and \( C=\{v, w, x, y, z\} \). List the members of the indicated set, using set braces. 11) (A \( \cup B)^{\prim2 answers -
Determina si es un Problema de Maximización Estándar. Maximizar \( G=-6 A+-1 B \) sujeto a \[ \begin{array}{l} -7 A+-4 B \leq 8 \\ -5 A+-3 B \leq 2 \\ A \leq 0, B \geq 0 \end{array} \] Cierto Falso2 answers -
\[ x^{-1}\left\{1 /\left(5\left(5^{2}+16\right)\right)\right\}= \] select the correct answer: \( a(1+\sin (4 t)) / 4 \) b. \( (1-\cos (4 t)) / 4 \) c. \( (1-\cos (4 t)) / 16 \) d. \( (1+\cos (4 t)) /2 answers -
2 answers
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2 answers
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Solve the differential equation for the expression given on the picture
5 [12 puntos] Resuelva la ecuación diferencial para \( \mathrm{f}(\mathrm{t}) \) si \( f(t)=3 t^{2}-e^{-t}- \) \[ \int_{0}^{t} f(u) e^{t-u} d u \]2 answers -
Find the solution of the differential equation if it is known to be a solution. (Hint: Order Reduction).
3. [8 pts.] Halla la solución de la ecuación diferencial \( x^{2} y^{\prime \prime}+x y^{\prime}+\left(x^{2}-\frac{1}{4}\right) y=0 \) si se sabe que \( y_{1}=x^{-1 / 2} \sin x \) es una solución.2 answers -
2 answers
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\( y^{(3)}-3 y^{\prime \prime}+9 y^{\prime}+13 y=0 \) \( c_{1} e^{x}+c_{2} e^{2 x} \cos 3 x+c_{3} e^{2 x} \sin 3 x \) \( c_{1} e^{-x}+c_{2} e^{2 x} \cos 3 x+c_{3} e^{2 x} \sin 3 x \) \( c_{1} e^{x}+c_2 answers -
Consider the differential equation dy/dx = 2(x - sqrt(x^2-y)) a) Set for which region in the R^2 plane the Value Problem Starts dy/dx = 2(x-sqrt(x^2-y)); y(x0) = y0 you will have a unique solution. Ex
[9 pts.] Considera la ecuación diferencial \( \frac{d y}{d x}=2\left(x-\sqrt{\left.x^{2}-y\right)}\right. \). a) [5 pts.] Establece para que región en el plano \( \mathbb{R}^{2} \) el Problema de Va2 answers -
Consider the following differential equation: a) Establish for what region of the plain R^2 will the initial value problem have a unique solution b) Verify that y1 = 2x and y2 = x^2 are solutions of t
1. [9 pts.] Considera la ecuación diferencial \( \frac{d y}{d x}=2\left(x-\sqrt{\left.x^{2}-y\right)}\right. \). a) [5 pts.] Establece para que región en el plano \( \mathbb{R}^{2} \) el Problema de2 answers -
\( y^{(3)}-3 y^{\prime \prime}+9 y^{\prime}+13 y=0 \) \( c_{1} e^{x}+c_{2} e^{2 x} \cos 3 x+c_{3} e^{2 x} \sin 3 x \) \( c_{1} e^{-x}+c_{2} e^{2 x} \cos 3 x+c_{3} e^{2 x} \sin 3 x \) \( c_{1} e^{x}+c_2 answers -
a) the points of equilibrium b) Draw the linear Phase diagram using the graph of the differential equation c) Establish the stability of the equilibrium points in part a
2. [10 pts.] El largo de un microtubo obedece la ecuación diferencial \[ \frac{d L}{d t}=-L(2-L)(1-L), \] donde \( L \) es medido en micrones y \( t \) es medido en segundos. a) [3 pts] ¿Cuáles son2 answers -
Find the solution of the differential equation bellow, if we know that y1 = x^2 is a solution (hint: order reduction and parameter variation)
3. [8 pts.] Halla la solución de la ecuación diferencial \( x^{4} y^{\prime \prime}+x^{3} y^{\prime}-4 x^{2} y=1 \) si se sabe que \( y_{1}=x^{2} \) es una solución. (Hint: Reducción de Orden y Va2 answers -
Consider a homogeneous differential equation with constant coeficientes whoes polinomial characteristics are given by the equation bellow a) what is the order of the following differential equation? b
[10 pts.] Considera una ecuación diferencial homogénea con coeficientes constantes cuyo polinomio característico está dado por: \[ P(r)=m^{2}(m+2)\left(m^{2}-1\right)\left(m^{2}+4\right)\left(m^{22 answers -
Find the solution of the following differential equation:
5. [8 pts.] Halla la solución de la ecuación diferencial \( y^{\prime \prime}-2 y^{\prime}+2 y=e^{x} \csc x \).2 answers -
Consider the differential equation dy/dx=2(x-sqrt(x^2 - y)) a) Establish for what region in the plane RR^2 the problem of initial value (dy/dx)= 2(x- sqrt(x^2 - y)); y(x0)=y0 will have a unique soluti
[9 pts.] Considera la ecuación diferencial \( \frac{d y}{d x}=2\left(x-\sqrt{\left.x^{2}-y\right)}\right. \). a) [5 pts.] Establece para que región en el plano \( \mathbb{R}^{2} \) el Problema de Va2 answers -
2. [10 pts.] El largo de un microtubo obedece la ecuación diferencial \[ \frac{d L}{d t}=-L(2-L)(1-L) \] donde \( L \) es medido en micrones y \( t \) es medido en segundos. a) [ 3 pts] ¿Cuáles son2 answers -
The solution for the differential equation is:
La solución de la ED \( 4 d y+y d x=x^{2} d y, y(4)=-1 \), es: a. \( (2+x) y^{4}+3 x-6=0 \) b. \( (2+x) y^{4}-3 x+6=0 \) c. \( (2+x) y^{4}+3 x+6=0 \) d. \( (2+x) y^{4}-3 x-6=0 \) Quitar mi elección2 answers -
Find the solution of the differential equation x^4y'' + x^3y' - 4x^2y = 1 if its known that y1=x^2 is a solution (Hint: Reduccion of Order and Variation of Parameters)
3. [8 pts.] Halla la solución de la ecuación diferencial \( x^{4} y^{\prime \prime}+x^{3} y^{\prime}-4 x^{2} y=1 \) si se sabe que \( y_{1}=x^{2} \) es una solución. (Hint: Reducción de Orden y Va2 answers -
Consider the differential equation a)Establish fot which region in the R^2 plane the initial value problem will have a unique solution.Explain b)Verify that y1=2x-1 and y2=x^2 are solutions of the di
1. [9 pts.] Considera la ecuación diferencial \( \frac{d y}{d x}=2\left(x-\sqrt{\left.x^{2}-y\right)}\right. \). a) [5 pts.] Establece para que región en el plano \( \mathbb{R}^{2} \) el Problema de2 answers -
A drug is infused into a patient's bloodstream at a constant rate of r grams per second.Simultaneously, the drug is removed at a rate proportional to the amount x(t) of the drug present at time t a)
2. [10 pts.] Un medicamento es infundido en el torrente sanguineo de un paciente a una tasa constante de \( r \) gramos por segundo. Simultáneamente, el medicamento es removido a una tasa proporciona2 answers -
Find the solution of the differential equation x^2y''+xy'+(x^2 -1/4)y=0 if it is known that y1=x^-1/2 sinx is a solution( hint: order reduction)
3. [8 pts.] Halla la solución de la ecuación diferencial \( x^{2} y^{\prime \prime}+x y^{\prime}+\left(x^{2}-\frac{1}{4}\right) y=0 \) si se sabe que \( y_{1}=x^{-1 / 2} \sin x \) es una solución.2 answers -
Consider a homogeneous differential equation with constant coefficients whose characteristic polynomial is given by a)What is the order of said differential equation? b) Find the general solution of
[10 pts.] Considera una ecuación diferencial homogénea con coeficientes constantes cuyo polinomio característico está dado por: \[ P(r)=m(m-3)\left(m^{2}+1\right)\left(m^{2}-4\right)\left(m^{2}+m+2 answers -
find the solution of the differential equation
5. [8 pts.] Halla la solución de la ecuación diferencial \( y^{\prime \prime}-2 y^{\prime}+2 y=e^{x} \csc x \).2 answers -
Solve \[ \begin{array}{l} {\left[\left(x^{\prime}\right),\left(y^{\prime}\right)\right]=[[3,1],[-25,-5]] \backslash[(x),(y)] \backslash \text { quad } x(0)=3, y(0)=-24} \\ x(t)^{\prime}= \end{array} \2 answers -
Part II: Evaluate f(2, 1) and f(2 1, 105) for the following two-vanable functions and calculate z Use total differentiation dz to approximate z 1. f(x, y) = 2x-3y 2. f(x,y) = ye^x Part III: 1. A righ
Parte II: Evalúe \( f(2,1) \) y \( f(2.1,1.05) \) para las siguientes funciones de dos variables y calcular \( \Delta z \) Utice la diferenciación total dz para aproximar \( \Delta z \) 1. \( f(x, y2 answers -
Find the solution of the differential equation y'' -2y'+2y=e^x cscx
5. [8 pts.] Halla la solución de la ecuación diferencial \( y^{\prime \prime}-2 y^{\prime}+2 y=e^{x} \csc x \).2 answers -
(1 point) Find the Jacobian. \( \frac{\partial(x, y, z)}{\partial(s, t, u)} \), where \( x=-(3 s+2 t+5 u), y=3 s+2 t+4 u, z=4 u-(4 s+t) \). \[ \frac{\partial(x, y, z)}{\partial(s, t, u)}= \]2 answers -
[9 pts.] Consider the differential equation !" !# = 2( − & $ − ). a) [5 pts.] Establish for which region in the plane ℝ$ the Initial Value Problem = 2( − & $ − ); ( %)
[9 pts.] Considera la ecuación diferencial \( \frac{d y}{d x}=2\left(x-\sqrt{\left.x^{2}-y\right)}\right. \). a) [5 pts.] Establece para que región en el plano \( \mathbb{R}^{2} \) el Problema de Va2 answers -
[9 pts.] Consider the differential equation a) [5 pts.] State for which region in the plane ℝ$ the Initial Value Problem will it have a unique solution. Explain b) [4 pts.] Verify that they are solu
[9 pts.] Considera la ecuación diferencial \( \frac{d y}{d x}=2\left(x-\sqrt{\left.x^{2}-y\right)}\right. \). a) [5 pts.] Establece para que región en el plano \( \mathbb{R}^{2} \) el Problema de Va2 answers -
6. Solve the initial value problem: \( y^{\prime \prime}+4 y^{\prime}+4 y=0, \quad y(0)=0, \quad y^{\prime}(0)=1 \)1 answer -
Question 18 Reaudva la curación diferencial de coeficientes, homogeners \( \left(y^{2}+y x\right) d x-x^{2} d y=0 \) usando ha sustitución Qustion 17 Resuctue la ecuación de Bermulli \( x^{2} \frac2 answers -
19 vi
9. Find \( \bmod z \) and amp \( z \) (principal amplitude) where (i) \( z=\frac{1+\sqrt{3} i}{1+i} \) (ii) \( z=\frac{-1+i}{1-\sqrt{3} i} \) (iii) \( z=1+i \tan \theta, \quad \frac{\pi}{2}2 answers