Perturbation Problem (ODE)

Question

Need answers to question 5a(iv), I'm confused whether it is regular perturbation or singular perturbation.

Also, 5b also.

Thank you.

Answer 1

If setting $\epsilon=0$ changes the character of the equation, then it is a singular perturbation. Thus a(iv) is singular, the order of the ODE changes from 2 to 1, while (iii) is regular, the ODE stays at order 2.

for b) one would need to know what techniques you know of. You can solve this via characteristic polynomial, via inner and outer solutions, via WKB approximation,...

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