For the equation ay" + by' + cy = 0, if b2 – 4ac = 0 (the repeated root case where the root is r = -b/2a) we learned that one solution is Y1 = e-bt/2a, and the second linearly independent solution is y, = te-bt/2a We were told that the second solution is found via the Reduction of Order method. Apply the Reduction of Order method to the equation using the first solution (Do the calculations, this will take about 5 or so minute Which of the following equations does it reduces to? au" + 2bu' -u + cu = 0 2a àu" – 2bu' +u + cu= 0 au" = 0 au" + 2bu' + u + cu = 0 O O O

Q: Identify b of the following quadratic equation: y = 2x2 +5x-14

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Q: Transform the equation -y^2+8y+x+12= 0 into its standard form

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Q: solve  w''' - 4w'' - 25w' + 100w = 0 how many linear independent solution to the equation needed…

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Q: Solve x = x + 2y and y = 2x + y with x(0) = 1 and y(0) = 2.

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Q: Locate root of the equation x +x- 2 = 0 using fixed point method.

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Q: Which equation is best to use to determine the zeros of the graph of y = 4z² – 8z – 5? - O (2r +…

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A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.