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Homework Statement
use the concept that y = c, -inf < x < inf is a constant function if and only if y' = 0 to determine whether the specified differential equation has any constant solutions:
y'' + 4y' + 6y = 10
The Attempt at a Solution
What throws me off in this particular problem is y''. If y' = 0 then y'' = 0 as well.
Only now when I integrate y'' to y' its y' = c1 so c1 = 0 and y' still = 0.
then I basically substitute my results in the equation to get:
(0) + 4(0) + 6(c) = 10
6c = 10
[c = 10/6, c1 = 0] are the constant solutions to the equation.
Does this make sense?
Thanks.