## MIT 1803 lecture 13

This lecture covered finding the , a particular solution of the ODE

Let the solutions be generally complex so that . Express the ODE as

let be or any polynomial operator on , then

which we will call the *substitution rule*. This yields the **exponential input theorem**

when . If , then the *exponential shift rule* can be used

In proving this rule – he again warns you not to hack your way forward – generating more work than necessary – make sure to use your previous result.

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