# 5th order DE with g(x)=32exp^(2x)

1. Feb 4, 2009

### leyyee

1. The problem statement, all variables and given/known data

Use variations of parameters to find the general solutions of the following differential equations.

y'''''-4y'''=32exp^(2x)

2. Relevant equations

no relevant equations.

3. The attempt at a solution

hey there, I tried solving this question. I got the homogeneous equation.

yh(x)=C1+C2x+C3X2+C4exp^(2x)+C5exp^(-2x)

but after this step.. I am stuck..

Because I am not quite sure whether I am in the correct path to look for the general solutions. After I have this equation, I did the wronskian matrix, I found the determinant of the 5X5 matrix is 512. Am I correct? Please correct me if I am not in the journey to my answer.

Besides that , If I were to use the variations of parameters. The matrix would be 5X5 dimensions. Is it correct?

Thanks

edited due to duplication on the template question.. sorry..

2. Feb 5, 2009

### Unco

You should get into the habit of reducing such a DE into something more familar. Let $$u=y^{(3)}$$, so the DE becomes $$u'' - 4u = 32e^{2x}$$.

Proceed as usual (involves a 2x2 matrix) to solve for u(x). Then you can obtain y(x).

3. Feb 5, 2009

### leyyee

hey there.

i will try out your attempt.. then i will post if i need anymore help..
thanks

4. Feb 5, 2009

### leyyee

hey there, i have tried out your attempt.. but I only can find the general solutions

the wronskians i found was -4, am I in the right path ?

u(x) = uh(x) + up(x) = C1e2x+C2e-2x+8xe2x-2e2x

how should I convert it to y(x) = yh(x) + yp(x)

If i use the equation u gave me u = y(3). Am I suppose to integrate u(x) by 3 times?

any clue for me?

thanks

Last edited: Feb 5, 2009
5. Feb 5, 2009

### Unco

Well done!

No need; you've done the variation of parameters work for u.

Exactly!

6. Feb 5, 2009

### leyyee

Wow.. thanks alot.. I think I will post the proper solutions after I finished the steps ok ?

and I will let you go through my answer to see whether I did any mistakes.. Thanks