Practice question · True or false
Two deposits obey the same ODE but start at different amounts. Their balance curves will eventually cross.
Hints
- Both curves are the same shape scaled by their starting values.
- One scaled copy of a positive curve can never overtake a larger one.
Show the answer
False
Why
Solutions of the same first-order ODE through different initial conditions never cross: both are with different , and their ratio stays constant forever. In pure compounding, a head start is permanent.
Practise Differential Equations
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