AC circuit to model blood flow - circuit analysis
By inspection, with the overall impedance of this circuit being Z
$$
I = P / Z = \dfrac{P}{r+\dfrac{1}{sC + 1/R }}=P\cdot\dfrac{sC+1/R}{r(sC+1/R)+1}
$$
Which is equivalent to
$$
  I \left( rsC+r/R+1 \right) = P (sC+1/R)
$$
So, your book is right.

In case you are not familiar with the Laplace transform you can replace the s with d/dt.