Can You Solve This Third Order Homogeneous Differential Equation?

[Saladsamurai]

Is this diff eq solvable? !

Homework Statement

Find the general solution to the third order homogeneous diff eq if one solution is known to be:

x^2e^{5x}


I was thinking of using reduction of order but I don't have the original equation!

 

[Saladsamurai]

Okay. Since it was given that the 3rd order diff eq is homogeneous, it is okay to assume that there is no particular solution to this, right?

And I can also assume that (m-5) is a factor of the characteristic equation. I am also assuming that it is a thrice repeated root, so y=c_1e^{5x}+c_2xe^{5x}+c_3x^2e^{5x}

I am not so confident in this, since it is all based on assumption. Any thoughts on the validity of this?

 

[d_leet]

It might help a bit if you told us what the differential equation was.

 

[Saladsamurai]

It might help a bit if you told us what the differential equation was.

Read the OP. It has not been given.

 

[HallsofIvy]

Okay. Since it was given that the 3rd order diff eq is homogeneous, it is okay to assume that there is no particular solution to this, right?

And I can also assume that (m-5) is a factor of the characteristic equation. I am also assuming that it is a thrice repeated root, so y=c_1e^{5x}+c_2xe^{5x}+c_3x^2e^{5x}

I am not so confident in this, since it is all based on assumption. Any thoughts on the validity of this?

Assuming this is a linear homogeneous 3^rd order diff eq with constant coefficients, then that is the case and the differential equation must be (D- 5)³y= y"'-15y"+ 75y'- 125y= 0. Of course, we were not told that.

 

[Saladsamurai]

So, as it stands, this problem has been worded incorrectly. That is what I thought. Thank you.