Practice question · True or false
The order of a differential equation determines how many independent constants its general solution carries.
Hints
- How many integrations does a second-order equation need?
- Each integration introduces one constant.
Show the answer
True
Why
True. Solving an th-order equation takes integrations, each contributing a constant, so the general solution has of them, and initial conditions are needed to pin them down. That is why a second-order equation of motion needs both an initial position and an initial velocity.
Practise Introduction to Differential Equations
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