Find the Wronskian: Solve for W(t) with y1=1 and y2=(2/9)-(2/9)e^(-9t/2)

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In summary, the conversation is about finding the Wronskian, a determinant of a 2x2 matrix of functions, for given values of y1 and y2. The person asking the question is unsure about how to do this and asks for help, but the person answering explains that it is a simple calculation and suggests looking up the definition for more information.
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Homework Statement



Find the Wronskian W(t)=W(y1,y2) where I have found y1=1 and y2=(2/9)-(2/9)e^(-9t/2)


The Attempt at a Solution



I am not sure how to do the Wronskian. We haven't talked about at all in class and I am not even sure what exactly it does. Any help would be greatly appreciated!

Thanks,
Joe
 
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The wronskian gives you information about the linear independence of y1 and y2. In spite of the fact it might sound complicated, it's REALLY easy. It's the determinant of a 2x2 matrix of functions. Why don't you look up the definition of wronskian and try it out?
 
  • #3


You're right! The calculation was simple. Thanks!
 

1. What is the Wronskian?

The Wronskian is a mathematical tool used to determine whether two functions are linearly independent or dependent. It takes the form of a determinant and is denoted by W.

2. How do I find the Wronskian?

To find the Wronskian, you must first determine the two functions involved. Then, you can set up a determinant using the derivatives of the functions and solve for the determinant value. In this case, the Wronskian can be found using the formula W(t) = y1(t)y2'(t) - y1'(t)y2(t).

3. What is the purpose of solving for W(t)?

Solving for the Wronskian can help determine if the two functions are linearly independent or dependent. If the Wronskian is equal to zero, then the functions are linearly dependent. If the Wronskian is not equal to zero, then the functions are linearly independent.

4. Can the Wronskian be used to solve for W(t)?

No, the Wronskian is a mathematical tool used to determine the linear independence of two functions. It cannot be used to solve for a specific function, such as W(t).

5. How does the given example of y1=1 and y2=(2/9)-(2/9)e^(-9t/2) relate to the Wronskian?

The given example can be used to calculate the Wronskian at a specific point in time, t. By plugging in the values of y1 and y2 into the Wronskian formula, you can determine whether the two functions are linearly independent or dependent at that point in time.

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