A Wronskian- variation of Params Problem

In summary, the conversation discusses solving a differential equation using the variation of parameters method and difficulty with the Wronskian. The speaker's solution manual does not use a Wronskian, but they end up with w=e^4x and w1=(-12e^4x)/(x^3) and w2=(12e^4x)/(x^4) for the derivative of the "constants". However, the integrals for u1 and u2 are deemed impossible at this point.
  • #1
Cocoleia
295
4

Homework Statement


y''-4y'+4y=(12e^2x)/(x^4)
I am trying to solve this differential equation. I know you would use the variation of parameters method, and I am trouble with the wronskian. My solution manual doesn't actually use a wronskian so I can't verify my work

Homework Equations

The Attempt at a Solution


I end up with w=e^4x
w1=(-12e^4x)/(x^3)
w2=(12e^4x)/(x^4)
But at this point the integrals for u1 and u2 seem rather impossible.
 
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  • #2
Cocoleia said:

Homework Statement


y''-4y'+4y=(12e^2x)/(x^4)
I am trying to solve this differential equation. I know you would use the variation of parameters method, and I am trouble with the wronskian. My solution manual doesn't actually use a wronskian so I can't verify my work

Homework Equations

The Attempt at a Solution


I end up with w=e^4x
w1=(-12e^4x)/(x^3)
w2=(12e^4x)/(x^4)
But at this point the integrals for u1 and u2 seem rather impossible.
Your Wronskian w=e4x is correct. but what are W1 and W2? What equations do you get for the derivative of the "constants"?
 
Last edited:

FAQ: A Wronskian- variation of Params Problem

1. What is a Wronskian- variation of Params Problem?

The Wronskian- variation of Params Problem is a mathematical concept used in differential equations. It involves solving for a set of parameters that satisfies a given differential equation and its boundary conditions.

2. How is the Wronskian- variation of Params Problem used in scientific research?

The Wronskian- variation of Params Problem is commonly used in scientific research, particularly in fields such as physics, engineering, and economics. It is used to model and analyze various physical systems and phenomena, such as heat transfer, fluid dynamics, and population growth.

3. What are the key components of the Wronskian- variation of Params Problem?

The key components of the Wronskian- variation of Params Problem include the differential equation, the boundary conditions, and the set of parameters being solved for. The Wronskian, a determinant formed from the solutions of the differential equation, is also an important component in solving this problem.

4. Is the Wronskian- variation of Params Problem difficult to solve?

The difficulty of solving the Wronskian- variation of Params Problem depends on the complexity of the differential equation and the number of parameters being solved for. In some cases, it can be solved analytically, but in many cases, numerical methods must be used to approximate the solution.

5. Can the Wronskian- variation of Params Problem be applied to real-world situations?

Yes, the Wronskian- variation of Params Problem has many practical applications and can be used to model and solve real-world problems. It is commonly used in engineering and scientific research to analyze and understand various physical systems and phenomena.

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