Suppose that m = 1 and k = 2 for the mass and spring of Example 3 and that the mass is attached also to a dashpot with damping constant c = 2. Then its displacement function x (t) satisfies the second-order equation x" (t) + 2x'(t) + 2x(t) = 0. With y = x' we obtain the equivalent first-order system dx = y, dt dy — — 2х — 2у dt

Q: 2. Solve the following simultaneous equations by elimination: (3x - y = 5 4x + y = 9 a) b) {3x 7x

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Q: . Describe and show two methods of solving the equation r – 5/I + 4 = 0

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Q: Solve a0 = 1, a1 = 3 and an = an−1 + 6an−2, for n ≥ 2.

A: We will start with the trial solution, an = rn for all n > 0

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Q: 36 – 4V3X+ 1 = 24

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Q: Solve for x.

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Q: dy e2x-y Q.2 Solve dx ex+y

A:

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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.