# Differential Calculus variaton of parameters question

• Ortix
In summary, the conversation discusses the process of solving the equation y'' - y' - 2y = 2e^(-t) by using the method of variation of parameters. It is mentioned that the derivatives of the u parameters are equated to 0 and the reason for this is unclear. The discussion also suggests that this may be a generalized approach and the solution can be found online.
Ortix

## Homework Statement

The equation that has to be solved:
y'' - y' - 2y = 2e^(-t)

The problem I am having is that I don't understand why they equatate that part with the derivatives of the u parameters to 0. (see image)

Here they first find the characteristic equation and write down the general solution. They then replace the constants with the parameter "u" and take the derivate.

As you can see, they just say that the derivate part of the u parameter is equal to 0. But why? How? Where did that come from? I can't find it anywhere in my book.

It's probably a facepalm answer but I would really appreciate it

Isnt the derivative of a constant zero?

yes but for some reason in the examples and solutions they even take the second derivative of u and they leave it in the equation. It's just that those 2 "parts" are equal to 0 for some reason that is unbeknownst to me and my buds here in the library..

they may be showing you generalized steps that you should keep in mind for the real world and then reducing them since the u1(t)=constant hence u1'=0 and u1''=0 ...

## What is differential calculus variation of parameters?

Differential calculus variation of parameters is a method used to solve non-homogeneous linear differential equations. It involves finding a particular solution by using a set of functions called variation of parameters.

## How is variation of parameters used in differential calculus?

In differential calculus, variation of parameters is used to find a particular solution to a linear differential equation by substituting a set of functions into the homogeneous solution. This method allows for a more general solution compared to other methods such as the method of undetermined coefficients.

## What are the steps involved in solving a differential calculus variation of parameters question?

The steps for solving a differential calculus variation of parameters question are as follows: 1. Find the homogeneous solution to the differential equation 2. Find the Wronskian of the homogeneous solution 3. Use the Wronskian to find the set of functions for variation of parameters 4. Substitute the set of functions into the homogeneous solution 5. Solve for the coefficients using integration 6. Add the particular solution to the homogeneous solution to get the general solution.

## What is the difference between variation of parameters and method of undetermined coefficients?

The main difference between variation of parameters and method of undetermined coefficients is that variation of parameters can be used to solve non-homogeneous linear differential equations with variable coefficients, while the method of undetermined coefficients is restricted to equations with constant coefficients.

## Are there any limitations to using variation of parameters in differential calculus?

Yes, there are limitations to using variation of parameters in differential calculus. It can only be used to solve linear differential equations and cannot be applied to non-linear equations. Additionally, it may not always be possible to find a particular solution using this method, in which case other methods may need to be used.

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