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Second Order Differential Equations
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Second order differential equations of the form dtd2x=f(x,dtdx,t), rewritten as the coupled system dtdx=y and dtdy=f(x,y,t) and solved using first order techniques.
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Second order differential equations
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A second order differential equation is a differential equation of the form
dtd2x=f(x,dtdx,t)
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,
⎩⎪⎨⎪⎧dtdx=ydtdy=f(x,y,t)
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.
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