Variation of Parameters Question

In summary, The conversation is about a question involving the use of Variation of Parameters to solve a problem. The person asking for help has tried to solve it but keeps getting the wrong answer. They provide their attempted solution and the correct answer, and ask for assistance. They also mention having a math final the next day.
  • #1
xlzhsteven
19
0
Question is attached as Clipboard01.jpg

I have tried the use Variation of Parameters to solve this question, but I kept getting wrong answer.
This is What I get y=(2e^x)(Cos(e^x))+0.5(e^(-x))Cos(e^(-x))-2Sin(e^(-x))
This is the right answer: y=-Sin(e^(-x))-(e^x)Cos(e^(-x))

Procedure is shown in the second jpg file
Can someone help me with this problem?
Thank You
 

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  • #2
Show how you got that answer and we will try to help.
 
  • #3
I have attached my procedure in scan0002.jpg
 
  • #4
Can anyone help me? I have math final tomorrow.
 

FAQ: Variation of Parameters Question

1. What is the "Variation of Parameters Question"?

The "Variation of Parameters Question" is a concept in mathematics that is used to find a particular solution to a non-homogeneous linear differential equation. It involves using a set of parameters to represent the unknown function, and then solving for those parameters.

2. How is the "Variation of Parameters Question" different from other methods of solving differential equations?

The "Variation of Parameters Question" is different from other methods of solving differential equations because it allows for finding a particular solution to a non-homogeneous equation, whereas other methods typically only find the general solution to a homogeneous equation.

3. What are the necessary conditions for using the "Variation of Parameters Question"?

The necessary conditions for using the "Variation of Parameters Question" include having a non-homogeneous linear differential equation, knowing the general solution to the corresponding homogeneous equation, and being able to find the Wronskian of the homogeneous equation.

4. What are the steps involved in solving the "Variation of Parameters Question"?

The steps involved in solving the "Variation of Parameters Question" include setting up the unknown function using a set of parameters, finding the Wronskian of the corresponding homogeneous equation, and then using the Wronskian and other known values to solve for the parameters.

5. How can the "Variation of Parameters Question" be applied in real-world situations?

The "Variation of Parameters Question" can be applied in real-world situations such as modeling the behavior of a spring-mass system, predicting population growth in a biological system, or analyzing the flow of electricity in a circuit. It is a useful tool for solving differential equations that arise in various scientific and engineering fields.

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