# Thread: [SOLVED] inhomogenous 2nd order D.e hard!

1. ## [SOLVED] inhomogenous 2nd order D.e hard!

Im not quite sure what trial particular integral to use for this equation $\displaystyle \frac{d^2y}{dx^2}-3\frac{dy}{dx}+2y=2e^x-5e^(2x)$ I get the complementary function to be $\displaystyle Ae^x+Be^(2x)$ Do i needto include a minus in my trial particular integral,,or an x^2? I wouldnt have thought i need a x^2 any ideas??

2. Not quite sure I know what you are asking.

$\displaystyle y"-3y'+2y=2e^{x}-5e$

Find the roots of the characteristic equation

$\displaystyle r^{2}-3r+2=0$ so, $\displaystyle r_{1}=1$ and $\displaystyle r_{2}=2$

Thus, the homogenous part of your equation is...

$\displaystyle y(t)=C_{1}e^{x}+C_{2}e^{2x}$

That looks like what you got. Is there more to the problem? Do you need to find the particular solution?

3. yeah thats right i just cant find the right trial solution to use that gives me the correct answer any ideas?

4. is this just a really hard question ,,my only problem is when originally there were two e^xs on the right hand side does the trial particular solution have to have two e^xs. The answer the book got was $\displaystyle y+Ae^x+Be^2x-2xe^x-5xe^2x$

5. Its not clear what the rhs of your eqn is.

Is it 2e^x -5e^(2x) ?

In this case :

i yp = Axe^x +B x e^(2x)

As e^x and e^(2x) are complimentary solutions

Similarly in the answer given do you mean - 5xe^(2x)

which would be consistent with i.

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