Practice question · Multiple choice
The general solution of a second-order ODE has two arbitrary constants, and a first-order one has a single constant. Why does the order fix the count?
Hints
- Count how many times you integrate to undo .
- Ask what you must know about a pendulum to predict its motion.
Show the answer
C. Because each integration introduces one constant
Why
Order equals the number of conditions needed. Newton's second law is second order, which is exactly why initial position and velocity, and nothing more, determine a trajectory.
Practise Second-Order Linear ODEs
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