Find the general solution to the following Cauchy-Euler equation ty" + ty' + 9y = – tan(3 ln t).

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A: See this solution in below.

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A: We have  this can be also written as

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Q: 5) des te = 5.] Save the operation cay-sity with glo = 1/2. x Cosy Siny

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Q: 7. Verify algebraically cos(0) sec(0) + sin(0) csc (0) = 1.

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Q: We have - (cos (u) du=

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Q: Solve the following equation y" – 2y' + y = Answer: y = C,e' + Czte' – e' In(1 + t²) + teʻ tan-i t

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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.