# "Use the differential operator method to find a fundamental set of solutions [...]"

• Oct 16th 2011, 09:42 PM
s3a
"Use the differential operator method to find a fundamental set of solutions [...]"
Could someone please tell me how to do this question so I can do the rest of them in my homework list? I know what the differential operator is from my book but I am not sure how to apply it in a problem.

Any input would be greatly appreciated!
• Oct 20th 2011, 01:13 PM
TheEmptySet
Re: "Use the differential operator method to find a fundamental set of solutions [...
Quote:

Originally Posted by s3a
Could someone please tell me how to do this question so I can do the rest of them in my homework list? I know what the differential operator is from my book but I am not sure how to apply it in a problem.

Any input would be greatly appreciated!

Since your question is not very clear I will take a stab at it.

$y''+14y'+49y=0$ can be written as
$D^2y+14Dy+49y=0 \iff (D^2+14D+49)y=0 \iff (D+7)^2y=0$
One such vector is $y=Ae^{-7x}$
You can also verify that $y=Bxe^{-7x}$ is in the kernel.
This will gives a spanning set $y_1=e^{-7x}, y_2=xe^{-7x}$