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MATH 325 Entire Course New > MATH 450 Entire Course New > Flashcards

MATH 450 Entire Course New Flashcards

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MATH 450 Week 1 Homework NEW

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MATH 450 Week 1 Homework NEW

MATH 450 Week 1 Homework NEW

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MATH 450 Week 1 Homework NEW

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MATH 450 Week 1 Quiz NEW

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MATH 450 Week 1 Homework NEW

MATH 450 Week 1 Homework NEW

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MATH 450 Week 1 Quiz NEW

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MATH 450 Week 2 Homework NEW

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MATH 450 Week 2 Homework NEW

MATH 450 Week 2 Homework NEW

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MATH 450 Week 2 Homework NEW

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MATH 450 Week 2 Quiz NEW

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MATH 450 Week 2 Quiz NEW

MATH 450 Week 2 Quiz NEW

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MATH 450 Week 2 Quiz NEW

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MATH 450 Week 3 Homework NEW

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MATH 450 Week 3 Homework NEW

1) The equations y1 = x^3 and y2 = x^5 form the basis of the second-order ODE x^2y” – 7xy’ + 15y = 0. Solve the initial value problem for the ODE given y(1)=0.4 and y’(1)=1
2) Find the general solution of the second-order ODE xy’’ + y’ = x^2 by reducing to first-order form
3) Find the general solution for the homogeneous linear ODE y” + 2.4y + 4y = 0. Verify your answer by substitution and using MATLAB
4) Solve the initial value problem for the ODE y” – 9y = 0 given the initial conditions y(0)=-2 and y’(0)=-12
5) Find the location of the maxima and minima of y= e^-2t. Round your answer to an accuracy of 2 decimal points. Hint: Recall from calculus that a maxima or minima of a function y occurs where the derivative of the function y’=0. In other words the slope of the function is 0
6) Find the general solution of a non-homogeneous ODE y” + 9y = cos(x) +IMG_256cos(3x)
7) Solve the initial value problem for the non-homogeneous ODE y” + 10y’ + 25 = 100sinh(5x)
8) Find the steady state current in the RLC circuit given below where R=8Ω, L=0.5H, C=0.1F and E=100sin(2t) V
9) Find the transient current (a general solution) in the RLC circuit given below given R=0.2Ω, L=0.1H, C=2F, and E=754sin(0.5t) V
10) Find the general solution of the non-homogeneous linear ODE y” – 2y’ + y = e^(x)sin(x) by variation of parameters

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MATH 450 Week 3 Homework NEW

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MATH 450 Week 4 Homework NEW

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MATH 450 Week 4 Homework NEW

1) Find an ODE for which the given functions e-2x, xe-2x, and x2e-2x form a basis of solutions.
2) Find an ODE for which the given functions cos(x), sin(x), xcos(x), and xsin(x) form a basis of solutions.
3) Obtain the general solution of the ODE yiv–29y”+100y=0.
4) Obtain a general solution of the ODE 4y”’+8y”+41y’+37y=0. Also solve the initial value problem given y(0)=9, y’(0)=-6.5, and y’’(0)=-39.75
5) Obtain the general solution of a non-homogeneous ODE [img width=”179” height=”22” src=”file://localhost/Users/mariangergi/Library/Caches/TemporaryItems/msoclip/0/clip_image002.gif” alt=”Описание: w4_hw_05” v:shapes=”Picture_x0020_1”>
6) Solve the initial value problem given the ODE yiv – 16y = 128cosh(2x) with initial conditions y(0)=1, y’(0)=24, y’’(0)=20, and y’’’(0)=-160
7) Are the given functions y1 = x+1, y2 = x+2 , and y3 = x linearly independent or dependent?
8) Apply the Euler method to solve the following initial value problem y’ = (y + x)2 given y(0)=0 and the step size h=0.1. Provide a table with the exact, calculated values, and the error for each step.
9) Apply the Euler method to solve the following initial value problem y’=(y+x)2 given y(0)=0 and the step size h=0.1. Provide a table with the exact, calculated values, and the error for each step.
10) Apply the classical Runge-Kutta method to solve the following initial value problem y’=(y+x)2 given y(0)=0 and the step size h=0.1. Provide a table with the exact, calculated values, and the error for each step

A

MATH 450 Week 4 Homework NEW

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7
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MATH 450 Week 3 Quiz NEW

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MATH 450 Week 3 Quiz NEW

.(TCO 2) Obtain the general solution of the second-order homogeneous ODE . Also obtain the particular solution given initial conditions and .

  1. (TCO 2) Find a particular solution of the second-order non-homogeneous ODE using the undetermined coefficients method.
  2. (TCO 2) Give a general solution to the non-homogeneous ODE .
  3. (TCO 2) Find current ‘I’ as a function of time t for the RLC circuit given below, if and . Hint: The standard form of ODE for the circuit is .
A

MATH 450 Week 3 Quiz NEW

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8
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MATH 450 Week 5 Homework NEW

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MATH 450 Week 5 Homework NEW

Homework Problem Work

  1. Find a general solution of the given ODE y’‘+15y’+50y =0 by converting it to a system. Verify the result using the previously known analytical method of solving second-order ODE.
  2. Find a general solution of the given ODE y’‘+2y’-24y = 0 by converting it to a system. Verify the result using the previously known analytical method of solving second-order ODE.
  3. Find a real general solution of the system:
  4. Convert the given ODE to a system form first and then determine the eigenvalues, coefficients p, q, and determinant . Determine the type of critical point based on these values.
  5. Find a general solution of the system:
A

MATH 450 Week 5 Homework NEW

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9
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MATH 450 Week 6 Quiz NEW

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MATH 450 Week 6 Quiz NEW

  1. (TCO 5) Apply the power series method to obtain the solution of . Compare this with the result obtained using MATLAB dsolve function.
  2. (TCO 5) Solve the initial value problem of using power series method given .
  3. (TCO 5) Using the Frobenius method, find a basis of solutions of the ODE:
  4. (TCO 5) Using the indicated substitutions , find a general solution of in terms of and .
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MATH 450 Week 6 Quiz NEW

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10
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MATH 450 Week 7 Homework NEW

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MATH 450 Week 7 Homework NEW

  1. (TCO 6) Find the Laplace transform of the function . Verify using MATLAB.
  2. (TCO 6) Find the Laplace transform of the function . Verify using MATLAB.
  3. (TCO 6) Using partial fractions method solve the initial value problem given and . Verify using MATLAB.
  4. (TCO 6) Using partial fractions method solve the initial value problem given and . Verify using MATLAB.
  5. (TCO 6) Solve the initial value problem for given and . Verify result using MATLAB.
  6. (TCO 6) Using the Laplace transform, solve the initial value problem:
A

MATH 450 Week 7 Homework NEW

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MATH 325 Entire Course New (10 decks)

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