Solving differential equations with second derivatives using a coupled system technique.
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Practice exam-style second order differential equations problems
A second order differential equation is a differential equation of the form
To solve these equations, we rewrite it as a system of coupled first order equations. Using the fact that dtd2x=dtd(dtdx) and substituting dtdx=y,
This equation can be solved with the usual techniques for coupled systems. On exams, questions involving second-order differential equations are usually set in a real-world context such as movement.