How to Solve Non-Homogeneous ODEs with Multiple Terms?

[benjamince]

Hi guys, this is my first post on the forums - I have a maths exam tomorrow and I'm pretty sure I will need to find the particular integral of a non-homogenous ODE. I find that pretty easy, but I'm not sure how to approach it when there are 2 different terms on the right:

d2y/dt2 - y = 1 + 3cos(2t)

or

(2)d2y/dt2 - dy/dt - y = t/2 + 3e(-t)

Any help would be much appreciated!
Thanks

Ben

 

[Gregg]

why don't you solve

$$\ddot{y}-y=1$$

$$\ddot{y}-y=3\cos(2t)$$

then add them together

 

[benjamince]

Oh ok that makes sense. It might seem silly, but I can do the second one, but I'm not sure what guess to use for the particular integral of 1?

 

[ross_tang]

You can try powers of x for the inhomogeneous function of 1.
$$Ax^2+Bx+C$$

If your exam allows, you may try the operator method. It works for all inhomogeneous function. You may refer to my tutorial in http://www.voofie.com" .

http://www.voofie.com/content/6/introduction-to-differential-equation-and-solving-linear-differential-equations-using-operator-metho/"

 

[benjamince]

Cool, thanks guys!