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ZixuanZhang
ZixuanZhang
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Integrating Factor

For , the integrating factor makes .

Example 4.16

Consider the equation

The integrating factor is

Therefore,

Remark. We require if we want to be finite as .

Radioactive decay

Example 4.17 (Radioactive Decay, Revisited)

We have

We can identify and . Thus, the integrating factor is

Hence,

Let us consider two cases.

  • If , then

    This is exactly the solution we arrived at in Example 4.15, using the PI and CF method.

  • If , then

    Thus,

    Note that the particular integral is now proportional to , which is different from the previous case. This is called the resonance case.

Related

Stated in