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Solve the differential equation \frac{1}{4}y'' +y' + y = x^2-2x by the method of undetermined...

Question:

Solve the differential equation {eq}\frac{1}{4}y'' +y' + y = x^2-2x {/eq} by the method of undetermined coefficients.

Method of Undetermined Coefficients:

To use the method of undetermined coefficients, we must be able to make a guess as to the form that the solution must take. For polynomials, the degree of the result can be no higher than the degree of the solution, so it is straightforward to make a guess about the solution.

Answer and Explanation:

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Since we must end up with a quadratic equation, we can assume that the solution is also a quadratic equation. Then in general it is of the form

{eq}\...

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Undetermined Coefficients: Method & Examples
Undetermined Coefficients: Method & Examples

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Chapter 10 / Lesson 15
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The method of undetermined coefficients is used to solve a class of nonhomogeneous second order differential equations. This method makes use of the characteristic equation of the corresponding homogeneous differential equation.


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