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Let us consider the following homogenous ODE of second order: $$x''(t)+a_1(t)x'(t)+a_2(t)x(t)=0$$ where $a_1$ and $a_2$ are continuous functions. Are there conditions on these functions such that one fundamental solution is increasing and the other fundamental solution is dercreasing.

Any ideas or sources on this are highly appreciated. Thanks in advance!

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