hahaha158 said:Homework Statement
solve 4y''-4y'+y=16et/2
Homework Equations
v1= -∫ y2g/w
v2= ∫ y1g/w
The Attempt at a Solution
http://imgur.com/gxXlfdH
the correct answer is 2t^2 e^(t/2) instead of what i have though, i am not sure what i am doing wrong?
The variation of parameters method is a technique used to find a particular solution to a 2nd order linear differential equation. It involves replacing the constants in the homogeneous solution with functions and then solving for those functions.
The variation of parameters method is different from other methods, such as the method of undetermined coefficients, in that it allows for a more general solution by incorporating arbitrary functions instead of just constants. This can be especially useful when dealing with non-homogeneous differential equations.
The first step is to solve the corresponding homogeneous equation and find the general solution. Then, we find the particular solution by replacing the constants in the general solution with functions and setting up a system of equations. Finally, we solve for the functions and substitute them back into the particular solution.
No, the variation of parameters method is only applicable to 2nd order linear differential equations. For non-linear equations, other methods such as the Euler method or Runge-Kutta methods may be used.
One limitation of the variation of parameters method is that it can become quite complex and tedious, especially when dealing with higher order differential equations. It also requires knowledge of solving systems of equations, which can be challenging for some. Additionally, it may not always yield a closed-form solution, which can be difficult to work with in some cases.