1. ## Answer to exam question correct?

Hi ,

i'm a first year student in biology from Brussels and, as most students do, have passed a math exam today. I'm not quite sure whether my solution to one of the questions is correct. I was wondering if somebody could check/confirm my answer? thx a lot ^^

The 2nd degree linear non homogenic DE is as follows :

y'' - 2y' - 3y = e^(-x)

Using the method of variation of parameters to find the particular solution Yp I found this general solution

Y = Yc + Yp = c1 e^(3x) + c2 e^(-x) – e^(-x)* ((1 + 4x) / 16)

Is this correct? I'm also wondering if I should have used the method of undetermined coefficients instead?

2. Originally Posted by pnklv
Hi ,

i'm a first year student in biology from Brussels and, as most students do, have passed a math exam today. I'm not quite sure whether my solution to one of the questions is correct. I was wondering if somebody could check/confirm my answer? thx a lot ^^

The 2nd degree linear non homogenic DE is as follows :

y'' - 2y' - 3y = e^(-x)

Using the method of variation of parameters to find the particular solution Yp I found this general solution

Y = Yc + Yp = c1 e^(3x) + c2 e^(-x) – e^(-x)* ((1 + 4x) / 16)

Is this correct? I'm also wondering if I should have used the method of undetermined coefficients instead?

Remember you can always check by plugging the solution into the ODE.

According to maple your solution checks and personally I would have used undetermined coefficeints but either way is correct.

3. Originally Posted by TheEmptySet
Remember you can always check by plugging the solution into the ODE.

According to maple your solution checks and personally I would have used undetermined coefficeints but either way is correct.

Thanks 4 check, life saver since the triple integral on my exam near dragged my points down below 12/20

Srry if this seems a stupid question, but what is ODE ( i assume a program/applet to calc DE's) & where can I find it ? ( might come in handy later )

4. Originally Posted by pnklv
Thanks 4 check, life saver since the triple integral on my exam near dragged my points down below 12/20

Srry if this seems a stupid question, but what is ODE ( i assume a program/applet to calc DE's) & where can I find it ? ( might come in handy later )
ODE means Ordinary differential equation.

What I ment is you cant take derivatives of your solution and plug them into the ode and check your solution. This is exactly like solving

$\displaystyle 2x+4=0 \implies x=2$

and plugging $\displaystyle x=2$ into it to check your solution.

IF you look at the attached immage above this code

Code:
  diff(y,x$2)-2*diff(y,x)-3*y means$\displaystyle y''-2y'-3y\$
and it did give the correct solution.