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# HW_11c - ¨ x b 2 x = 0 with x(0 = 1 and ˙ x(0 = 0 Once...

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Homework #11c: Symbolic 3 Reading: Handout Homework: This assignment will be done entirely in the MATLAB command window. Be sure to make clear your answers and give any explanation / additional work that is asked for. Turn problems in IN THE ORDER THEY ARE ASSIGNED. Each problem needs to be labeled so the TA can find your work. Complete the following problems: 1. Use the Matlab function solve to find the roots of the following system(s) of equations: (a) ax 2 + bx + c = 0, Hopefully you already know this solution but use MATLAB to verify. (b) x 5 + 3 x 4 - x 2 - 5 x + 10 = 0 (c) xy 2 - x 3 y - y = 0, Solve in terms of x (i.e. y = y ( x )). (d) 3 x + 5 y = 4 - 2 x - y = 2 (e) a + b + c = 3 - 2 a + b - 2 c = 0 3 a - 3 b + c = 1 2. Use the Matlab function dsolve to solve the following differential equation:
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Unformatted text preview: ¨ x + b 2 x = 0 with x (0) = 1 and ˙ x (0) = 0. Once you have the solution for x ( t ), plot the result with b = 5 for ≤ t ≤ 5. 3. Use Matlab symbolic tools to ﬁnd at what x value the minimum of y = x 2-2 x + 5 occurs. Also, evaluate the function at the minimum. 4. Use Matlab symbolic tools to ﬁnd at what x values the two optimal points of y = x 3-4 x 2 + x + 3 occur. Determine which point is a minimum and which is a maximum. Also, evaluate the function at the minimum and maximum. Verify your results by plotting y from-2 ≤ x ≤ 4....
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