Consider the DE d'y + 16- + 64y = I dz2 dr hich is linear with constant coefficients. irst we will work on solving the corresponding homogeneous equation. The auxiliary equation (using m as your variable) is = 0 which has root Because this is a repeated root, we don't have much choice but to use the exponential function corresponding to this root to do reduction of order. 8z 2 = ue Then (using the prime notation for the derivatives) So, plugging Y2 into the left side of the differential equation, and reducing, we get

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A: topic - differential equation

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Q: Find the Wronskian of two solutions of the differential equation t²y" — t(t — 5)y' + (t− 2)y = 0…

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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.