Category Archives: MATH 450

MATH 450 Week 3 Homework Latest Work

MATH 450 Week 3 Homework Latest Work

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MATH 450 Week 3 Homework Latest Work

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

MATH 450 Week 3 Quiz Latest Work

MATH 450 Week 3 Quiz Latest Work

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MATH 450 Week 3 Quiz Latest Work

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

2.(TCO 2) Find a particular solution of the second-order non-homogeneous ODE using the undetermined coefficients method.

 

3.(TCO 2) Give a general solution to the non-homogeneous ODE .

 

4.(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 .

MATH 450 Week 4 Homework Latest Work

MATH 450 Week 4 Homework Latest Work

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MATH 450 Week 4 Homework Latest Work

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

MATH 450 Week 5 Homework Latest Work

MATH 450 Week 5 Homework Latest Work

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MATH 450 Week 5 Homework Latest Work

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:

 

6. 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.

 

7. Find a general solution of the system:

MATH 450 Week 6 Quiz Latest Work

MATH 450 Week 6 Quiz Latest Work

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MATH 450 Week 6 Quiz Latest Work

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 .

MATH 450 Week 7 Homework Latest Work

MATH 450 Week 7 Homework Latest Work

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MATH 450 Week 7 Homework Latest Work

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.

 

9.(TCO 6) Using the Laplace transform, solve the initial value problem: