수학 질문... 급해요.

[As an individual.. I proceed]

공식을 깜빡해서... 좀 풀어주세요. ㅠㅠ

면목이 없네요. 정말 죄송합니다. 이번만 부탁할게요.

책이 다 영어로 써 있어서.. particular solution, indicial equation,

recurrence relation 같은 걸 뭐라고 해야 되는 지..

수학 고수님들은 다 아실테지만.. -_- 풀어주시면 정말 감사하겠습니다.

For the differential equation 6xy'' - 3y' + 6y = 0, x = 0 is a regular singular point.

a. Find the indicial equation.

b. Find the recurrence relation.

c. Find the first four terms of a series solution corresponding to the roots of

the indicial equation from part (a).


lb = pound ft = feet


A 128-pound weight is attached to a spring whose spring constant is 20 lb/ft

a) Write down the differential equation that describes simple harmonic motion (or

free undamped motion) of this spring-mass system. Use x(t) to denote the

displacement of the spring from the equilibrium position.

b) What is the frequency of simple harmonic motion in part (a)?

c) Write down the corresponding differential equation if the driving (external)

force F0(sin At) acts on the spring-mass system in part (a)

d) For what values of parameter F0 and A does the resonance occur?

e) Find a particular solution of the differential equation from part (c) in the

resonance case.