Verify a Fundamental Set of Solutions for a Linear Second Order Homogeneous DE

This video provides an example on how to verify two functions form a fundamental set of solutions. The general solution is also found.
Site: mathispower4u.com

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[@stephb4658]

Can you explain at 3:39 more? The exponent (x/2) times derivatives of x should be 1/2e^x/2? not e^x/2

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[@jr-1754]

what if they are linearly dependent? meaning they equal 0

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