Is My Work Correct for These Particular Solutions?

  • MHB
  • Thread starter shamieh
  • Start date
In summary, particular solutions in science serve the purpose of providing precise and accurate answers to specific problems or equations. They can be found through various mathematical methods, simulations, or experiments. These solutions can be applied to real-life situations and are often used in scientific research. However, they are not always unique and may not always accurately represent the real world due to simplifications and limitations in resources and data.
  • #1
shamieh
539
0
I just need someone to verify that my work is correct.

Note that the general solution to $y'' - y = 0$ is $y_h = C_1e^t + C_2e^{-t}$

In the following, use the Method of Undetermined Coefficients to find a particular solution.
b) $y'' - y = 4sint + 2cost$

Solution:
$y_p = -cost - 2sint$
c)$y'' - y = e^t$

Solution:
$y_p = \frac{1}{2} te^t$

d) Give a particular solution to $y'' - y = t^2 + 4sint + 2cost + e^t$

Solution:
$ y_p = -t^2-2 -cost - 2sint + \frac{1}{2}te^t$
 
Physics news on Phys.org
  • #2
Yes, that's correct. (Yes)
 

FAQ: Is My Work Correct for These Particular Solutions?

What is the purpose of finding particular solutions in science?

Particular solutions in science are used to solve specific problems or equations in a given context. They provide a more precise and accurate answer compared to general solutions, which may not take into account all relevant factors.

How do you find particular solutions in science?

To find particular solutions in science, you must first identify the specific problem or equation that needs to be solved. Then, you can use mathematical methods such as substitution, elimination, or graphing to find the particular solutions. In some cases, computer simulations or experiments may also be used to find particular solutions.

Can particular solutions be applied to real-life situations?

Yes, particular solutions can be applied to real-life situations. In fact, they are often used in scientific research to study and understand various phenomena in the natural world. By finding particular solutions, scientists can make predictions and develop practical applications to solve real-world problems.

Are particular solutions always unique?

No, particular solutions are not always unique. Some equations may have multiple particular solutions, while others may have no particular solutions at all. It depends on the complexity of the problem and the available data. In some cases, there may be an infinite number of particular solutions.

What are the limitations of finding particular solutions in science?

One limitation of finding particular solutions is that they may not always accurately represent the real world. This is because scientific models and equations are simplifications of complex systems, and there may be other factors at play that are not accounted for. Additionally, finding particular solutions may require a high level of mathematical proficiency and may not always be feasible due to limited resources or data.

Back
Top