Solving Nonhomogeneous Linear ODEs using Annihilators - Comments

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  • #3
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Great entry! Please make some more math tutorials Mark!!
 
  • #4
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Great entry! Please make some more math tutorials Mark!!
Thank you! I have another one in mind coming soon, and probably some more after that.
 
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  • #5
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I think I found 2 small typos in the post. In ex 1, you said
Mark44 said:
Substituting back into the original differential equation, I get

##9c_1e^{3t}+c_2e^t–4(3c_1e^{3t}+c_2e^t)+3(A+c_1e^{3t}+c_2e^t)=5

⇒(9c_1–12c_1+3c_1)e^{3t}+(c_2–4c_2+c_2)e^t+3A=5

⇒A=5/3##
I think in the 2nd last step ##(c_2–4c_2+3c_2)e^t## should be over there instead of ##(c_2–4c_2+c_2)e^t##.

In ex 4, you said
Mark44 said:
With a fourth-order equation, we expect the fundamental solution set to consist of four linearly independent solutions: {##e^{−t},te−t,cos(2t),sin(2t)## }.
The 2nd solution should be ##te^{-t}## right?
 
  • #6
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I think I found 2 small typos in the post. In ex 1, you said

I think in the 2nd last step ##(c_2–4c_2+3c_2)e^t## should be over there instead of ##(c_2–4c_2+c_2)e^t##.

In ex 4, you said

The 2nd solution should be ##te^{-t}## right?
Thanks for spotting these -- I have fixed both of them.
Even though I looked through this stuff before publishing it, it's still hard to catch everythin, especially when you're working with LaTeX .
 

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