2nd order ODEs in Python - defining the differential

Question

I have the following differential equation:
y"(t)+b*y'(t)+a*y(t)=c(p(t)-p0)

with initial values y(0), y'(0). y(t) is to be found.
There are several ways to solve it, but my problem was with defining the following function based on it:
def Function(y,t):
    b=2
    a=3
    c=1
    pT=4
    p0=1
    dydy=-b*dy-a*y-c*(pT-p0)
    return dydy

dy is obviously not defined - how is it possible to define it?

Lutz Lehmann · Answer

Your state vector has two components, so the function you have to pass to odeint should be
def Function(y,t):
    ...
    return [ y[1], c*(pT-p0) - b*y[1]-a*y[0] ]

that is, also return the tuple of the derivatives of the two state components.

Allen Han · Answer

If you have y'(0) you can use that as the value for dy. Also, your notation is odd. y'(t) is not dy. y'(t) is dy/dt. Below, I have used yprime instead of dy.
Your function should probably be
def findYDoublePrime(y, yprime):
    b=2
    a=3
    c=1
    pT=4
    p0=1
    return -b*yprime-a*y-c*(pT-p0)

2nd order ODEs in Python - defining the differential

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