To solve an initial value problem for a second-order nonhomogeneous differential equation, we’ll follow a very specific set of steps. We first find the complementary solution, then the particular solution, putting them together to find the general solution. Then we differentiate the general solution, plug the given initial conditions into the general solution and its derivative to create a system of linear equations, and then use the initial conditions to solve that system for the constant coefficients. Finally, we’ll plug those constant coefficients back into the general solution.

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