Find Wronskian of {e^(x)*cos(sqrt(x)), e^(x)*sin(sqrt(x))} Homework

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Homework Help Overview

The problem involves finding the Wronskian of the functions {e^(x)*cos(sqrt(x)), e^(x)*sin(sqrt(x))}. The original poster attempts to apply the Wronskian formula and simplify the expression but arrives at a different result than expected.

Discussion Character

  • Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the Wronskian formula and the simplification process. There are suggestions to improve the clarity of mathematical expressions by using LaTeX.

Discussion Status

The discussion includes attempts to clarify the mathematical expressions and a realization from the original poster about an error in their calculations. Guidance on using LaTeX has been provided, but no consensus on the Wronskian result has been reached.

Contextual Notes

There is a mention of the original poster's mistake in their calculations, but the specific nature of the mistake is not detailed. The conversation also highlights the importance of formatting in mathematical communication.

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Homework Statement


Find the Wronskian of {e^(x)*cos(sqrt(x)), e^(x)*sin(sqrt(x))}.

Homework Equations


W(f, g)=fg'-gf'

The Attempt at a Solution


W(f, g)=(e^(x)*cos(sqrt(x)))(e^(x)*cos(sqrt(x))*1/(2x^1/2))-(e^(x)*sin(sqrt(x)))(-e^(x)*sin(sqrt(x))*1/(2x^1/2)+e^(x)*cos(sqrt(x)))
After simplifying this, I got (e^(2x)(1-2*sqrt(x)*sin(sqrt(x))*cos(sqrt(x)))/(2x^(1/2)). But the correct answer is e^(2x)/(2x^1/2).
 
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It would help a lot if you edited your post to use latex for your math expressions.
 
I agree. With almost 250 posts, it is time to learn latex.
 
Never mind, I found the mistake in my problem.
 

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