Question: Q1 The differential equation + () + () = 0 is known as a homogeneous second-order linear equation. It contains (second order). The

Q1

The differential equation " + () + () = 0 is known as a homogeneous second-order linear equation.

It contains " (second order). The terms ", and all have an exponent of 1 (linear). And the right hand side of the equation is 0 (homogeneous).

Prove: if 1() and 2() are two solutions for this equation, then any linear combination of these two functions, 1 () + 2(), is also a solution.

Q2

You have to find the series expansion for the function

(around = 0)

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