Linear Second-Order Differential Equations Part 2: Non-Homogeneous Differential Equations

We just learned how to solve homogenous linear second-order differential equations. Now it’s time to tackle the non-homogenous variety. This will start out the same way that we learned in the previous tutorial, but that will get us something called the complementary solution. Then we have to add to that a particular integral, depending on the function on the right side of the equation. This can be done by two methods. We can use the method of undetermined coefficients, which will involve selecting a trial function, or we can perform the variation of parameters, by calculating something called the Wronskian. It’s hard to explain, let me just show you!

Script by Lorcan Nicholls

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