Math 225 Differential Equations Notes Chapter 2

Theorem 2.1 Existence and Uniqueness Theorem
Suppose P (x) and Q(x) are continuous on an interval (a, b)
that contains the point x 0 . Then for any choice of initial values
y 0 there exist a unique solution y(x) on (a, b) to the initial value
problem
• dy
dx
+ P (x)y = Q(x)
• y(x 0 ) = y 0
In fact the solution is:
y(x) = 1
µ(x)
for the appropriate C.
[∫
]
µ(x)Q(x) + C
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