Diff eq: I dont understand my prof's comments. Here is my work.

[frozenguy]

So I had an exam and got this problem wrong, that I had done incorrectly on the quiz as well. comments in red under picture are comments from professor.

here is the work:

Attempt)

Why is this general solution? What is the fundamental set? What is y_p? (this should be verified)

So on the exam, in addition to what I did, I should of found the first, second, and third derivatives of each y_1,2,3 and then separately substitute them into the non homogeneous eqn to check for validity?

And uh, WOW. I could of sworn I wrote out y_p.. So if write y_p=2x-12x²e^x that would satisfy that part right?

 

[rock.freak667]

I think your professor wanted you to start with the differential equation and work to get the general solution rather than substituting the equation they gave you into the DE.

 

[Dickfore]

You found y₁, y₂ and y₃, but did not identify y_p.

You showed that y₁, y₂ and y₃ are linearly independent, but you did not show that each one is a particular solution to the homogeneous equation.

Finally, you should have shown that y_p is the particular solution to the non-homogeneous equation.

 

[frozenguy]

I think your professor wanted you to start with the differential equation and work to get the general solution rather than substituting the equation they gave you into the DE.

Ok thanks!

1.)You found y₁, y₂ and y₃, but did not identify y_p.

2.)You showed that y₁, y₂ and y₃ are linearly independent, but you did not show that each one is a particular solution to the homogeneous equation.

3.)Finally, you should have shown that y_p is the particular solution to the non-homogeneous equation.

So maybe like this?