Numerical solutions of differential equations

# MATHEMATICAL METHODS OF Science and Engineering #http://www1.uprh.edu/rbaretti # http://www1.uprh.edu/rbaretti/methodsoftheoreticalphysics.htm # http://www1.uprh.edu/rbaretti/methodsoftheoreticalphysicsPart2.htm # http://www1.uprh.edu/rbaretti/methodsoftheoreticalphysicsPart3.htm # http://www1.uprh.edu/rbaretti/methodsoftheoreticalphysicsPart4.htm # http://www1.uprh.edu/rbaretti/methodsoftheoreticalphysicsPart5.htm # Lectures on Quantum Mechanics http://www1.uprh.edu/rbaretti/LQMIntro.htm # http://www1.uprh.edu/rbaretti/LQMch1.htm #http://www1.uprh.edu/rbaretti/LQMch2.htm # http://www1.uprh.edu/rbaretti/LQMch3.htm # http://www1.uprh.edu/rbaretti/LQMch4.htm # http://www1.uprh.edu/rbaretti/LQMch5.htm #www.geocities.com/serienumerica4 #www.geocities.com/serienumerica3 #www.geocities.com/serienumerica2 #www.geocities.com/serienumerica #www.geocities.com/fisicageneral2009 # example 1rst order DE dx/dt= -x+1 t = var('t') # define a variable t x = function('x',t) # define x to be a function of that variable DE = lambda y: diff(y,t) + y - 1 desolve(DE(x(t)), [x,t]) 

e^(-t)*(e^t + c)

e^(-t)*(e^t + c)

# example 2nd order DE d^2x/dt^2= -x+1 t = var('t') # define a variable t x = function('x',t) # define x to be a function of that variable DE = lambda y: diff(y,t,2) + y - 1 desolve(DE(x(t)), [x,t]) 

k1*sin(t) + k2*cos(t) + 1

k1*sin(t) + k2*cos(t) + 1

# example 2nd order DE d^2x/dt^2 + dx/dt +x =0 t = var('t') # define a variable t x = function('x',t) # define x to be a function of that variable DE = lambda y: diff(y,t,2) + diff(y,t) - y desolve(DE(x(t)), [x,t]) 

k1*e^((sqrt(5) - 1)*t/2) + k2*e^((-sqrt(5) - 1)*t/2)

k1*e^((sqrt(5) - 1)*t/2) + k2*e^((-sqrt(5) - 1)*t/2)

 

Traceback (click to the left of this block for traceback)
...
NameError: name 'k1' is not defined

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/sage/sagenb/sage_notebook/worksheets/reibaretti/28/code/10.py", line 7, in <module>
    x=k1*e**((sqrt(_sage_const_5 ) - _sage_const_1 )*t/_sage_const_2 ) + k2*e**((-sqrt(_sage_const_5 ) - _sage_const_1 )*t/_sage_const_2 )
NameError: name 'k1' is not defined