Question

Let M be the integer corresponding to the first letter of your last name. For example, if your last name begins with "A", M=1 and if your last name begins with "Z", M=26.

Let k=1/M and consider the logistic equation dy/dt = k y (M - y).

Construct a single figure including

1. Title "Logistic Equation Slope Field and Euler's Method solutions by FirstName LastName" with your actual first and last names, along the top
2. Labels for the axes
3. a slope field for -3 ≤ t ≤ 3, -M/2 ≤ y ≤ 3M/2
4. Euler's method solutions for initial conditions   y(0)=5M/4, y(0)=M, y(0)=M/2, y(0)=0 and y(0)=-M/4, in each case for -3 ≤ t ≤ 3, h=0.1
5. For each initial condition, a label "y(0) = (value)" but with the actual value, at an appropriate location
6. For each solution curve, a label "y(3) ≈ (Euler's method value)" but with the actual value, or "y(3) = ?", at an appropriate location

Last name starts with a P

Answer 1

ANSWER:

Given That Let M be the integer corresponding to the first letter of your last name. For example, if your last name begins with "A", M=1 and if your last name begins with "Z", M=26.

Let k=1/M and consider the logistic equation dy/dt = k y (M - y).

So the python code is:

# FB - 201104096
import science
# initial Order lyric (y' = f(x, y)) problem solver victimization mathematician methodology
# xa: initial price of experimental variable
# xb: final price of experimental variable
# ya: initial price of variable quantity
# n : variety of steps (higher the better)
# Returns price of y at xb.
def Euler(f, xa, xb, ya, n):
h = (xb - xa) / float(n)
x = xa
y = ya
for i in range(n):
y += h * f(x, y)
x += h
return y

# Second Order lyric (y'' = f(x, y, y')) problem solver victimization mathematician methodology
# y1a: initial price of calculation of variable quantity
def Euler2(f, xa, xb, ya, y1a, n):
h = (xb - xa) / float(n)
x = xa
y = ya
y1 = y1a
for i in range(n):
y1 += h * f(x, y, y1)
y += h * y1
x += h
return y

if __name__ == "__main__":
print Euler(lambda x, y: math.cos(x) + science.sin(y), 0, 1, 1, 1000)