Solving Differential Equation Sympy

问题

I haven't been able to find particular solutions to this differential equation.

from sympy import *

m = float(raw_input('Mass:\n> '))
g = 9.8
k = float(raw_input('Drag Coefficient:\n> '))
v = Function('v')
f1 = g * m
t = Symbol('t')
v = Function('v')
equation = dsolve(f1 - k * v(t) - m * Derivative(v(t)), 0)
print equation

for m = 1000 and k = .2 it returns

Eq(f(t), C1*exp(-0.0002*t) + 49000.0)

which is correct but I want the equation solved for when v(0) = 0 which should return

Eq(f(t), 49000*(1-exp(-0.0002*t))

回答1:

I believe Sympy is not yet able to take into account initial conditions. Although dsolve has the option ics for entering initial conditions (see the documentation), it appears to be of limited use.

Therefore, you need to apply the initial conditions manually. For example:

C1 = Symbol('C1')
C1_ic = solve(equation.rhs.subs({t:0}),C1)[0]

print equation.subs({C1:C1_ic})

Eq(v(t), 49000.0 - 49000.0*exp(-0.0002*t))

来源：https://stackoverflow.com/questions/38950163/solving-differential-equation-sympy