(19) (a) Suppsoe that y is a solution of the differential equation ay" + by+cy 0. Let 2(r) = y(r-ro) where ro is an arbitrary real mumber. Show that a:" + be' +es =0. (b) Let a() (r- ro) and s2() = va(* - ro), where va = Cn + can in the general solution to ap by +cy-0. Show that sa- +a is abo a general solution of ay" + by + cy -0.

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: Explanation of the answer is as follows

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Q: Verify that the indicated function y p(x) is an explicit solution of the given first-order…

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A: Here we use the basic definitions of singular point

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A: Topic = Differential equation

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A: To explain why

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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.