Toronto Math Forum
MAT2442013S => MAT244 MathLectures => Ch 3 => Topic started by: Jeong Yeon Yook on February 11, 2013, 10:46:40 PM

In equation (28) of theorem 3.6.1, it says that "where t0 is any conveniently chosen point in I".
This is for the integral limits for u1 and u2.
I don't understand how we can just conveniently choose some t0 for the general solution when it's not an initial value problem.

In equation (28) of theorem 3.6.1, it says that "where t0 is any conveniently chosen point in I".
This is for the integral limits for u1 and u2.
I don't understand how we can just conveniently choose some t0 for the general solution when it's not an initial value problem.
Looking for a general solution we can select initial point as we please; it definitely affects other constants. Look at
\begin{equation*}
\int_{t_0}^f f(t)\,dt'+C_0=\int_{t_1}^f f(t)\,dt'+C_1
\end{equation*}
as long as $C_1C_0=\int_{t_0}^{t_1}f(t')\,dt'$ and you can select any initial point $t_0$.