Variation of parameters. unsure why my solution differs from professor's

In summary, the conversation was about finding the general solution for the equation 2y'' - 3y' + y = ((t^2) + 1)e^t. The person provided their particular solution, but the expert advised to check the solution by substituting back into the original equation. The expert also pointed out a mistake in the copied professor's solution.
  • #1
fufufu
17
0

Homework Statement


what is general solution of 2y'' - 3y' + y = ((t^2) + 1)e^t

Homework Equations



my particular solution is: (e^t) ((2/3)(t^3) + 6t -4))
prof particular solution is: ((1/3)(t^3)(e^t)) - 2(t^3)(e^t) + 9(te^t)

The Attempt at a Solution


here is how i solved , i hope this is ok to post link tp pdf..its faster than typing this all out..
https://docs.google.com/open?id=0BwJqUg33PgREQTFaejBCUkRRWlNfRW9maU1oaDNYQQ

thanks for any help/advice/hints
 
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  • #2
You can check if your solution is correct by substituting back into the original equation. ehild
 
  • #3
As the coefficient of y'' is not 1 in the original equation, you have to divide the right-hand side by 2 when calculating u' and v'.

I think you did not copy your professor's solution correctly. It has to be
(1/3 t3-2t2+9t)et.

ehild
 
Last edited:

FAQ: Variation of parameters. unsure why my solution differs from professor's

1. What is the concept of variation of parameters?

Variation of parameters is a mathematical method used to solve non-homogenous linear differential equations. It involves finding a particular solution by introducing a set of arbitrary constants and then using these constants to find the general solution.

2. How does variation of parameters differ from other methods of solving differential equations?

Variation of parameters differs from other methods, such as the method of undetermined coefficients, in that it allows for a more general solution. It also does not rely on guessing a particular solution, making it a more systematic approach.

3. What are the steps involved in using variation of parameters to solve a differential equation?

The first step is to find the general solution to the associated homogeneous equation. Then, a particular solution is introduced by assigning arbitrary constants to each term in the general solution. These constants are then substituted into the non-homogeneous equation, and a system of equations is set up and solved for the constants. Finally, the general solution and the particular solution are combined to obtain the complete solution.

4. Why might my solution differ from my professor's when using variation of parameters?

There could be several reasons for this. It is possible that you made a mistake in your calculations, or you may have used different arbitrary constants. It is also important to note that there can be multiple correct solutions to a differential equation, so your solution may differ from your professor's but still be valid.

5. Are there any limitations to using variation of parameters?

Yes, variation of parameters can only be used to solve linear differential equations with non-homogeneous terms. It also requires the associated homogeneous equation to have a known general solution. Additionally, it may not always be the most efficient method for solving a differential equation, as it can involve complex calculations.

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