What should I try for the particular integral inorder to solve these problems where D means d/dx.

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- Nov 8th 2008, 04:14 AMroshanheroSecond order differential equations
What should I try for the particular integral inorder to solve these problems where D means d/dx.

- Nov 8th 2008, 06:43 AMPeritus
- Nov 8th 2008, 07:02 AMroshanhero
But I couldnot get it still.

- Nov 8th 2008, 07:29 AMChris L T521
Are you familiar with the so-called "Annihilator" approach?? To see how you do it this way, look at post #7 in my differential equations tutorial [also look at post #6 and #8 for two other techniques].

Going along with this, we solve the homogeneous solution first:

You should end up with

Now for the particular solution, solve the non homogeneous equation.

This will lead us to finding the annihilator of , which is

The DE becomes with multiplicity six. Thus, the particular solution with only consist of r repeating 4 times, since 2 were used in the homogeneous solution.

Thus,

Now substitute into the original DE and find the coefficients...

Quote:

Try to do something similar to what I have done above.

I hope this helps.

--Chris