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' Solving dy/dx = 7*y^2 * x^3 with start condition y(2) = 3 

def f1(x,y) = 7*y^2 * x^3

y0 = 3
x0 = 2
yf = 0
xf = 1 
maxseg = 10000
maxerr = 0.001
errcode = 0

diffeqn x0, y0, xf, maxseg, maxerr, yf, errcode USE f1(x,y)

' Exact solution for comparision
def g1(x) = -1 / (7/4 * x^4 - 85/3)

print "g1(xf) = "; g1(xf)
print "yf(xf) = "; yf

if(errcode != 0) then
    print "Error solving equation"
    print "Increasing maxseg might help"
endif

' Defining the differential equation for a stiffness system

def f2(y,t) = -1000*y + 3000 - 2000 * exp(-t)

' Solving equation at time tf = 0.001 seconds with y(0) = 0
y0 = 0
t0 = 0
yf = 0
tf = 0.001 
maxseg = 1000
maxerr = 0.001
errcode = 0

diffeqn t0, y0, tf, maxseg, maxerr, yf, errcode USE f2(y,t)

' Exact solution for comparision
def g2(t) = 3 - 0.998*exp(-1000*t) - 2.002 * exp(-t)

print "g2(tf) = "; g2(tf)
print "yf(tf) = "; yf

if(errcode != 0) then
    print "Error solving equation"
    print "Increasing maxseg might help"
endif