https://en.wikipedia.org/wiki/Windkessel_effect So I'm doing a mini research project (TIPE) for french entrance exams. And I came across this blood flow modelization which involves some differential equations like: ${\displaystyle (1+{R_{1} \over R_{2}})I(t)+(R_{1}C+{L \over R_{2}}){dI(t) \over dt}+LC{d^{2}I(t) \over dt^{2}}={P(t) \over R_{2}}+C{dP(t) \over dt}}$
My questions are: could I actually solve this equation (assuming I have sufficient initial conditions) without having another equation that relates $P(t)$ to $I(t)$? Do solutions for this kind of equation even exist? If yes, is it analytically solvable? N.B: I don't know much about differential equations except the basic ones like linear first order equations and linear second order equations with constant coefficients and zero for right-hand side. I appreciate any help :)