1. ## Non-Homogeneous DQ's

Hello, I am having some trouble with these second and third order non-homogeneous dq's.

I can identify a Y compliment, but I freeze up when I have to distinguish the Y particular.

ex 1) Solve:

y'' - y' = 11x + 1

Ycompliment -

(D^2 - D)y = 0
D(D-1)y = 0

Roots: D= 0, 1

Yc = c1 *e^0x + c2 *e^x = 1 + c2 *e^x

Now this is where I get lost... I can ID Yc but not Yp. Please help! Thanks!

2. For the particular integral try $y = ax^2 + bx$

Bobak

3. Thanks for the help!

One question, how do you arrive at this solution? If you could explain further, the process, I would greatly appreciate it!

I understand that it's more of a guessing thing, but how should I make the best guess?

Thanks again, Chris

4. Originally Posted by ccdelia7
Thanks for the help!

One question, how do you arrive at this solution? If you could explain further, the process, I would greatly appreciate it!

I understand that it's more of a guessing thing, but how should I make the best guess?

Thanks again, Chris
It is not guessing at all. From the differential equation it should be obvious that the particular integral is a polynomial, in which case all you need to determine is the order of the polynomial, Can you explain why such a polynomail for this differential equation must have a zero ceofficient on any terms higher than $x^2$?

Bobak

5. Originally Posted by bobak
For the particular integral try $y = ax^2 + bx$

Bobak
Actually you can get away with $y = ax^2 + bx + c$

-Dan

6. Originally Posted by topsquark
Actually you can get away with $y = ax^2 + bx + c$

-Dan
No point there is a constant term in the complementary solution.

Bobak