Solving Nonhomogeneous Linear ODEs using Annihilators - Comments

[Mark44]

Mark44 submitted a new PF Insights post

Solving Nonhomogeneous Linear ODEs using Annihilators

Continue reading the Original PF Insights Post.

 

[eltodesukane]

Nice review! Some more here: http://jekyll.math.byuh.edu/courses/m334/handouts/annihilator.pdf

 

[PWiz]

Great entry! Please make some more math tutorials Mark!

 

[Mark44]

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.

 

[PWiz]

I think I found 2 small typos in the post. In ex 1, you 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

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?

 

[Mark44]

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 .