4.2.1.4 Example 4 \(y^{\prime }=8+3F\left ( 3x+5y+9\right ) \)

\[ y^{\prime }=8+3F\left ( 3x+5y+9\right ) \]

Comparing the above to (1) shows that

\begin{align*} B & =8\\ C & =3\\ a & =3\\ b & =5\\ c & =9 \end{align*}

Plugging these into (2A) gives

\begin{align*} \int \frac {du}{bB+bCF\left ( u\right ) +a} & =x+c_{1}\\ \int \frac {du}{40+15F\left ( u\right ) +3} & =x+c_{1}\end{align*}

Where in the above \(u=3x+5y+9\).