Why ignores constant when applying integral into differential-equation.? I studied how to draw 'Direct-form I' and 'Direct-form II' from differential equation.

The book taught me like this:

$$\mbox{Give equation: }{a_0}{y(t)}+{a_1}{y'(t)}+{a_2}{y''(t)} = {b_0}{x(t)}+{b_1}{x'(t)}+{b_2}{x''(t)}$$



step 1. change from differentiator into integrator, because integrator is cheaper than differentiator.

\begin{array}{}
{a_0}{y^{(2)}(t)}+{a_1}{y^{(1)}(t)}+{a_2}{y(t)} = {b_0}{x^{(2)}(t)}+{b_1}{x^{(1)}(t)}+{b_2}{x(t)} &amp;
\begin{cases}
x^{(i)} \mbox{ is i-times integral of x}\\
y^{(i)} \mbox{ is i-times integral of y}
\end{cases}
\end{array}

step 2. change form like this: $y(t)=...$

\begin{array}{}
\displaystyle y(t)=\frac{1}{a_2}\left( {b_0}{x^{(2)}(t)}+{b_1}{x^{(1)}(t)}+{b_2}{x(t)}-{a_0}{y^{(2)}(t)}-{a_1}{y^{(1)}(t)}\right)
\end{array}

step 3. draw




My question is why doesn't consider constant value in step 1?
The constants would be the initial conditions, such as an initially charged capacitor or an inductor with an initial current. If all constants are set to zero it means that you have zero initial conditions, which is usually the standard assumption unless stated otherwise.