Interpretation of ODE Question

[Ry122]

Hi

Could someone please help me to understand what questions a) and b) here are asking for?

 

[Simon Bridge]

Pretty much means what it says:
It wants you to prove that (1) is a solution to the DE given, and then prove that (1) is actually the general solution.

 

[Ry122]

Okay well for a) I'm guessing you would do this by deriving the eigen-equation.

But for b) how would you show that it's not just 'a' solution but is the general solution?

 

[Simon Bridge]

Okay well for a) I'm guessing you would do this by deriving the eigen-equation.

There is no need to derive anything - the equations are given to you. Though you do need to be able to express the relationship between A and it's eigenvectors algebraically.

But for b) how would you show that it's not just 'a' solution but is the general solution?

Use the definition of "general solution".
What is the difference between a specific solution and the general solution of any DE?

All this is stuff you should have covered way back when you 1st learned about 1st and 2nd order ODE's - before you ad to deal with systems of ODEs like above. It is just the same.