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I'm kind of new to differential equations and I was looking at differential inequalities. I was wondering if I had a second-order differential inequality of the form $f''(x) + af'(x) + b \leq 0$ where $a$ and $b$ are constants, what values for $a$ and $b$ would require f(x) to decay or grow exponentially? I've found some criteria for exponential growth, but I'm wondering if there is any literature on this that could help me out. Thanks.

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