Existence and uniqueness for linear ﬁrst order ode in y

3.1.2 Existence and uniqueness for linear ﬁrst order ode in $y$

3.1.2.1 Example 1
3.1.2.2 Example 2
3.1.2.3 Example 3
3.1.2.4 Example 4

These are ode’s in the form

y^{'} + p (x) y = q (x)

The theorem says that if both $p (x), q (x)$ are continuous at $x_{0}$ then solution exists and is unique. Notice that now we do not check on $y_{0}$ but only on $x_{0}$ . We get both existence and uniqueness all in one test. If either $p$ or $q$ are not continuous, then no guarantee solution exist or be unique.

[prev] [prev-tail] [front] [up]

3.1.2 Existence and uniqueness for linear ﬁrst order ode in y

3.1.2 Existence and uniqueness for linear ﬁrst order ode in $y$