Is there a way to verify the correctness of decoupled linear ODE solutions?

[SteliosVas]

Okay so i have 2 ODE's i need to decouple them and therefore construct two differential equations each containing just one of the functions... I just wanted to know how can you verify you have the correct solution is more so my question

du/dt= 4u-5v

dv/dt=2u-3v

I end up getting

for u(t) = Ae^x + Be^-3x

and for v(t) = Ae^5x +Be^x

My question is also when assigning the solutions to the characteristic equation do you give the higher number to a and the lower to b??

THanks :)

 

[Geofleur]

You can check your solutions by substituting them back into the original problem. For example, if you calculate $du/dt$ using your expression for $u$, then that should be equal to $4u-5v$ using both your expressions for $u$ and for $v$. I think you will find that your solution is not correct.

 

[Mark44]

Okay so i have 2 ODE's i need to decouple them and therefore construct two differential equations each containing just one of the functions... I just wanted to know how can you verify you have the correct solution is more so my question

du/dt= 4u-5v

dv/dt=2u-3v

I end up getting

for u(t) = Ae^x + Be^-3x

and for v(t) = Ae^5x +Be^x

My question is also when assigning the solutions to the characteristic equation do you give the higher number to a and the lower to b??

As already stated by Geofleur, your solutions don't work. Did you solve this system by matrix diagonalization? If so, please show us your work in getting the eigenvalues.

 

[HallsofIvy]

As Geofleur and Mark44 say, you do not have the correct solutions to the equations. You should have arrived at a characteristic equation $r^2- r- 2= 0$.

But to answer your question, "A" and "B" are both unknown constant coefficients. It doesn't matter which you assign to which exponential.