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natka813 [3]
3 years ago
14

Please help asap. will give brainliest to first answer.

Mathematics
1 answer:
pentagon [3]3 years ago
6 0

Answer:

it is the 3rd one :)

Step-by-step explanation:

i had that exact same question im pretty sure :o

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Step-by-step explanation:

Let y1 and y2 be (e^x)/2, and (xe^x)/2 respectively.

The Wronskian of them functions be

W = (y1y2' - y1'y2)

y1 = (e^x)/2 = y1'

y2 = (xe^x)/2

y2' = (1/2)(x + 1)e^x

W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)

= (1/4)(x + 1 - x)e^(2x)

W = (1/4)e^(2x)

Since the Wronskian ≠ 0, we conclude that functions are linearly independent, and hence, form a set of fundamental solutions.

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Answer:

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Step-by-step explanation:

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