How can you possibly make a Second Order Constant Coefficient Differential Equation question challenging? Would anyone like to share a challenging problem (no modelling please).

Question

How can you possibly make a Second Order Constant Coefficient Differential Equation question challenging? Would anyone like to share a challenging problem (no modelling please).

anonymous · Answer

@amistre64
@satellite73 
@experimentX
@eliassaab 
@dpaInc

anonymous · Answer

I am talking about those types of problem sets that ask you:

a) Solve the differential equation 

and/or

b) Solve the initial value problem

anonymous · Answer

If it's homogenous with constant coefficients it's pretty much destined to be really easy, except maybe some that have imaginary roots; but they still aren't that hard. Nonhomogenous ode are more difficult. Give this one a shot, I just copy and pasted from my old ode book.

$$y''+3y'=2t^4+t^2\exp(-3t)+\sin(3t)$$

anonymous · Answer

@abstracted 
- why are there y's on one side, but no y's for the other?

anonymous · Answer

oh never mind I don't do homogeneous. Only the type that I mentioned.

anonymous · Answer

@abstracted that would just be tedious x.x Guess the solution to be in the form:
$$At^4+Bt^3+Ct^2+Dt+E+(Ft^2+Gt+H)e^{-3t}+I \sin(3t)+J \cos(3t)$$

anonymous · Answer

And just hope there aren't any repeat roots :P Or just be a boss and covert it over to a first order system and use some matrix calculus xDD