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2 changes: 1 addition & 1 deletion book_src/chapters/chapter1.do.txt
Original file line number Diff line number Diff line change
Expand Up @@ -55,7 +55,7 @@ in this book are initial value problems. As an example, consider the very simple
\[ u'=u .\]
!et
This equation has the general solution $u(t)=Ce^t$ for any constant $C$, so it has an infinite number of solutions.
Specifying an initial condition $u(t_0)=u_0$ gives $C=u_0$, and we get the unique solution $u(t)=u_0e^t$.
Specifying an initial condition $u(0)=u_0$ at time $t_0 = 0$ gives $C=u_0$, and we get the unique solution $u(t)=u_0e^t$.
We shall see that, when solving the equation numerically, we need to define $u_0$ in order to start our method and
compute a solution at all.

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