i did the first part and it is correct, i do not know the interval. i Think it i

Question

i did the first part and it is correct, i do not know the interval. i Think it is (2, inf) but the transient i have no idea. please help with that thanks

Find the general solution of the given differential equation. (x2-4) dr + 4y = (x + 2)2 x 2 Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.) (-2,2) x Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated ist; if there are none, enter NONE.) x +2 x + 2

Explanation / Answer

The solution is correct as y(x) = (C+x)(x+2)/(x-2)

The largest interval of the definition of the solution is R-{2} , i.e., (-infinity,2) U (2,infinity) since except the point 2, the solution is well defined.

The transient term is defined as the term which tends to 0 as x tends to infinity. Here, the only transient terms is 2C/(x-2) which tends to 0 as x tends to infinity. The other 3 terms in the solution however does not satisfy this

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