Get questions and answers for Advanced Math

Advanced Math Archive: Questions from May 09, 2023

• 
  

  
  \( \frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x}+5 y=2 e^{-2 x} \sin 3 x \)
  2 answers
• 
  

  
  1. Find the general solution for the following homogenous differential equations: 1. \( y^{\prime \prime}-6 y+10 y=0 \) 2. \( y^{\prime \prime}-3 y^{\prime}=0 \) 3. \( y^{\prime \prime}+6 y^{\prime}+9
  2 answers
• 
  

  
  Problem 11. Let \[ f(x)=\sum_{k=1}^{\infty} \frac{\cos (k x)}{k^{2}} \] Prove that \[ \int_{0}^{\pi / 2} f(x) d x=\sum_{k=0}^{\infty} \frac{(-1)^{k}}{(2 k+1)^{3}} \]
  2 answers

• 

  
  Consider the system of non-linear differential equations \[ \begin{array}{l} \frac{d x}{d t}=x \sin y, \\ \frac{d y}{d t}=y \cos x . \end{array} \] Which one option gives the Jacobian matrix for this
  2 answers

• 

  
  Solve Laplace's equation, \( \frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}=0,0
  2 answers
• Find the general solution of the following problem: Answer is C, just show procedures on getting to the general solution
  Cuál de las siguientes opciones contiene la solución general a: \[ \begin{array}{l} -16 y+x y^{\prime}=x^{18} e^{9 \mathrm{x}} \\ y=\mathrm{C} x^{16}+\frac{1}{81} x^{16} e^{9 x}+\frac{1}{9} x^{17} e
  2 answers
• ​​​​​​​
  1. Which of the mappings defined on the Cartesian plane by the equations below are transformations? \[ \begin{array}{lll} x((x, y))=\left(x^{3}, y^{3}\right), & \beta((x, y))=(\cos x, \sin y), & \gamm
  2 answers
• 1. Completely factor the polynomial: 2x2+6x+4. 2. Extract the FCM (Common Major Factor) from the following exercise: 4x3y-6x2y+3xz. 3. Calculate the following polynomial (x6+6x3+2x+4) + (x6+5x3-89x+
  1. Factorice completamente el polinomio: \( 2 x^{2}+6 x+4 \). 2. Extraiga el FCM (Factor Común Mayor) del siguiente ejercicio: \( 4 x^{3} y-6 x^{2} y+3 x z \). 3. Calcule el siguiente polinomio \( \l
  2 answers
• 8. Trace the graph of the equation: y = 3x+1. • Complete the following table by filling in the empty spaces using the equation: y = 3x+1: 9. Get the slope of the line that passes through the poin
  8. Trace la gráfica de la ecuación: \( \mathbf{y}=3 \mathrm{x}+1 \). - Complete la siguiente tabla llenando los espacios vacios utilizando la ecuación: y= \( 3 x+1 \) : 9. Obtenga la pendiente de
  2 answers
• 
  

  
  \( 1,5,11,15,21,25,31,35,41,45,53,57,61,65,67 \) Find \( \frac{d y}{d x} \) 29. \( \frac{d}{d x}\left(-2 \sqrt[3]{x^{3}}\right) \) 1. \( y=x^{7} \) 2. \( y=x^{8} \) 3. \( y=-3 x \) 4. \( y=-0.5 x \) 3
  2 answers
• Solve the following differential equation. 9ty 1 + t² ○ y = = 1/(¹+1²) 4+0 ¥+C (1+t²) 2 y = -(1+²) ³+C (1+1²)⁹ y = -t²-t+C (1+t²)⁹ y = y = = 2 (1+1²) ¹0 + C (1+1²)⁹ -(1+²) ³+C (
  Solve the following differential equation. \[ \frac{d y}{d t}+\frac{9 t y}{1+t^{2}}=-1 t \] \[ \begin{array}{l} y=\frac{-\frac{1}{11}\left(1+t^{2}\right)^{\frac{11}{2}}+C}{\left(1+t^{2}\right)^{\frac{
  2 answers
• short distance from A to J
  Para el siguiente grafo, ¿cuál es la ruta de menos distancia entre A y J?
  2 answers
• 
  

  
  \[ \begin{array}{l} U=\{q, r, s, t, u, v, w, x, y, z\} \\ A=\{q, s, u, w, y\} \\ B=\{q, s, y, z\} \\ C=\{v, w, x, y, z\} \end{array} \] the elements in the set. A. \( \{r, z, t, u, v, w, x, z\} \) B.
  2 answers
• #4.) pick any letter. show all work
  4. Solve the homogeneous linear differential equation with initial conditions: a. \( y^{\prime \prime}-10 y^{\prime}+25 y=0: \quad y(0)=1, y(1)=0 \) b. \( y^{\prime \prime}-4 y^{\prime}+5 y=0: \quad y
  2 answers
• 
  

  

  
  Calculate all four second-order partial derivatives of \( f(x, y)=(5 x+3 y) e^{y} \). \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \] Calculate \( T_{2}(t, y) \),
  2 answers
• 
  

  
  

  
  \[ \begin{array}{l} U=\{q, r, s, t, u, v, w, x, y, z\} \\ A=\{q, s, u, w, y\} \\ B=\{q, s, y, z\} \\ C=\{v, w, x, y, z\} \end{array} \] Let List the elements in the set. \( (A \cap B)^{\prime} \) A. \
  2 answers
• 
  

  
  \[ \begin{array}{l} U=\{q, r, s, t, u, v, w, x, y, z\} \\ A=\{q, s, u, w, y\} \\ B=\{q, s, y, z\} \\ C=\{v, w, x, y, z\} \end{array} \] Let List the elements in the set. \( (A \cup B)^{\prime} \)
  2 answers
• 
  

  
  Let \( U=\{q, r, s, t, U, v, w, x, y, z\} \) \[ \begin{array}{l} A=\{q, s, u, w, y\} \\ B=\{q, s, y, z\} \\ C=\{v, w, x, y, z\} \end{array} \] List the elements in the set. \( A^{\prime} \cup B \) A.
  2 answers
• 
  

  
  SESIÓN N० 02 TEMA: ECUACION DE LEGENDRE \[ \left((x+1)^{2} D^{2}+(x+1) D-1\right) y=\operatorname{Ln}(x+1)^{2}+x-1 \]
  2 answers