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# General solution of equation watch

1. I was wondering if some one could check my answer here...currently working through Engineering Mathematics book. I am imposing the conditions I have two different ways, the latter I do not understand perhaps some guidance will be helpful.

The question is ;

Find the general solution of the equation

Assume that y(0) = 3 and y'(0) = 1 to find particular solution.

-----------------------------------------------------------------------------------

Auxiliary equation

Roots

So the general solution is or

Now to find the particular solution I impose the conditions

y(0) = 3 gives 3 = A + B
y'(0) = 1 gives 1 = 1A - 1B

A + B = 3
3A + 3B = 9
-------------------
-B = 12
B = -12
A - 12 = 3
A = 3

On the other hand if

Then for y'

Calculating with all this stuff is somewhat confusing, any advice? is my final answer correct?
2. Your auxiliary equation isn't correct. But your method is spot on. I think pluggin in the numbers you're given and finding simultaneous equations is fine, you just have to be careful that you have the right solutions.
3. Incorrect, surely?
4. Yah, my brain working faster than my hands syndrome . Tend to forget to negate.
5. (Original post by insparato)
Your auxiliary equation isn't correct. But your method is spot on. I think pluggin in the numbers you're given and finding simultaneous equations is fine, you just have to be careful that you have the right solutions.
In this case the auxillary equation cant be consisting of a complex-conjugate....can it, because its greater >0 ?
6. y'' + 2y' + y = 0

Auxiliary -> m^2 + 2m + 1 = 0

Nope! Not complex.
7. (Original post by insparato)
y'' + 2y' + y = 0

Auxiliary -> m^2 + 2m + 1 = 0

Nope! Not complex.
doh! silly me thanks insparato.

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