|May13-12, 10:50 PM||#1|
DE with a constant
My math is a little rusty - so please bear with me if this is a stupid question.
I know how to solve both homogenous and non-homogenous DEs
However, I am not sure where a DE with a constant falls & how to solve it.
y'' + 2y' + c = 0
(c is a constant).
You cannot convert this into an algebraic equation in r like you do for regular homogenous DEs. So what's the method for solving this?
If this is a different category of DEs (i.e. neither homo nor non-homo), then even giving me the name of this type of DE is good enough - I can google and find the method.
An example of this type of DE is a bar loaded with a uniformly distributed load of f.
The DE is
AEu'' + f = 0
u -> deflection.
f is a constant.
|May13-12, 11:12 PM||#2|
You can solve the equation y'' + 2y' = -c. This is a non homogenous equation where the non-homogenous part is a constant. So the general solution is
-((c x)/2) - 1/2 exp(-2 x) C + C
where C and C are constants.
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