mmont012 said:Homework Statement
Use the method of variation of parameters to find a particular solution
Homework Equations
https://flic.kr/p/NqhtyQ
The Attempt at a Solution
https://flic.kr/p/NicCbN
[/B]
Can some find my mistake? The answer is just suplosed to be - 2/3te^-t[/B]
I second what Ray said. Although the image of your work that you posted is reasonably neat, many people post images that are blurry or messy or otherwise difficult to read. One of the main problems with work posted in images rather than as text here in the input pane, is that people responding can't insert a comment at the point where an error lies, but instead have to describe the location of the error.Ray Vickson said:You should type out the problem and your solution. Just posting images is strongly discouraged on this Forum.
The variation of parameters method is a technique used in solving differential equations, where the particular solution is expressed as a linear combination of the solutions to the homogeneous equation. This method is useful when the coefficients of the differential equation are not constant.
The variation of parameters method is different from other methods, such as Euler's method or Runge-Kutta method, because it allows for the particular solution to be expressed as a linear combination of the solutions to the homogeneous equation. This allows for a more general solution to be found, rather than just a numerical approximation.
The steps involved in using the variation of parameters method are as follows:
1. Solve the homogeneous equation to find the complementary solution.
2. Find the Wronskian of the homogeneous equation.
3. Use the Wronskian to find the coefficients in the particular solution.
4. Substitute the particular solution into the original equation and solve for the remaining coefficient.
5. Combine the complementary solution and particular solution to get the general solution.
No, the variation of parameters method can only be used for linear differential equations with non-constant coefficients. It cannot be used for nonlinear or partial differential equations.
Some common mistakes made when using the variation of parameters method include:
- Forgetting to find the Wronskian of the homogeneous equation
- Using the wrong formula to find the coefficients in the particular solution
- Making errors in the integration process
- Forgetting to include the constant of integration in the particular solution