3.3 Nonhomogeneous Linear Second-order Differential Equations A. General Solution of Nonhomogeneous Equations. In this section, we explore the nonhomogeneous linear second-order differential equation of the form:. Example 2. Find the general solution of the equation. Solution. We will use the method of undetermined coefficients. The right side of the given equation is a linear function Therefore, we will look for a particular solution in the form. Then the derivatives are. Substituting this in the differential equation gives: The last equation must be.
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First I found solution for the homogeneous equation, it is a repeated root so. yp = Ax2ln(x) + Bx2. Here for the nonhomogenous equation, I used parameter variation: y1 = x2lnx and y2 = x2. Using Wronski and Cramer rules: yp = u1. y1 + u2. y2. W = det [ x2lnx x2 2xlnx + x 2x] = − x3. Integrate to find u1, u2.. The widget will calculate the Differential Equation, and will return the particular solution of the given values of y (x) and y’ (x) Get the free “Non-Homogeneous Second Order DE” widget for your website, blog, WordPress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha.