# Math Help - particular integral

1. ## particular integral

i have the following system of differential equations:

x = 3x + 2y + 4e-t
y = x +4y +10

I am after a particular integral of this system. I think the answer is:

[x y] = [ae-t b]

(i think this is meant to be a general answer not specific - its a multiple choice answer)

Does any one else agree?

The other option i thought was

[x y] = [ae-t + b 0] so that the constant in the second equation reduces to zero.

2. Hello

it is not a system of differential equations ! Where are x'(t) and y'(t) ??

3. sorry they are first order differentials there should be a dot above the x and y

4. Originally Posted by thermalwarrior
sorry they are first order differentials there should be a dot above the x and y
There are a few x's and y's in the equations you've given ....... It would be best if you made appropriate edits to the original post. Use x' and y' to represent the derivatives.

5. the equations should read

x = 3x + 2y + 4e-t

y = x + 4y + 10

x and y left hand side have dots above them

6. i have had another a look at this question and does this make any more sense:

x' = 3x + 2y + 4e-t
y' = x + 4y + 10

with a complementary function of [x y] = a[1 1]e^5t + b[-2 1]e2^t

has the particular integral

[x y] = [ae-t + b ce-t + d]