Existence and Uniqueness Theorem for general first-order equations
Theorem: Let the functions f and
be continuous in some rectangle
containing the point
(t0,y0). Then, in some interval
t0 - h < t < t0 + h contained
in
,
there is a unique solution
of
the initial value problem
Other differences found when dealing with non-linear equations:
Even if a solution is found, it may be difficult to determine the interval where the solution is valid
A general solution may not provide every solution
Solutions found are often implicit rather than explicit
Numerical approximations are of great importance