Euler Implícito

Y_{0} = 1 (slider from -5 to 5)
a = 1 (slider from -5 to 5)
T: 1 / a
h = 1.5 (slider from 0 to 3)
A = Intersect(xAxis, yAxis)
B = Point(Circle[A, (8 * h)])
f = Segment(A, B)
C = Midpoint(A, B)
D = Midpoint(A, C)
E = Midpoint(C, B)
F = Midpoint(A, D)
G = Midpoint(D, C)
H = Midpoint(C, E)
I = Midpoint(E, B)
g = OrthogonalLine(F, xAxis)
i = OrthogonalLine(D, xAxis)
j = OrthogonalLine(G, xAxis)
k = OrthogonalLine(C, xAxis)
l = OrthogonalLine(H, xAxis)
m = OrthogonalLine(E, xAxis)
n = OrthogonalLine(I, xAxis)
p = OrthogonalLine(B, xAxis)
J = Point(Circle[A, T])
q = Segment(A, J)
K = Point(Circle[J, T])
r = Segment(J, K)
s = OrthogonalLine(J, xAxis)
t = OrthogonalLine(K, xAxis)
f_1(x) = (Y_{0} * ℯ^(((-a) * x)))
g_1(x) = ((-Y_{0}) * ℯ^(((-a) * x)))
L = Intersect(f_1, yAxis, (0, 1))
c = Circle(F, Distance[A, L] / (1 + (a * h)))
M, N = Intersect(c, g)
d = Circle(D, Distance[F, N] / (1 + (a * h)))
O, P = Intersect(d, i)
e = Circle(G, Distance[D, P] / (1 + (a * h)))
Q, R = Intersect(e, j)
c_1 = Circle(C, Distance[G, R] / (1 + (a * h)))
S, U = Intersect(c_1, k)
d_1 = Circle(H, Distance[C, U] / (1 + (a * h)))
V, W = Intersect(d_1, l)
e_1 = Circle(E, Distance[H, W] / (1 + (a * h)))
Z, A_1 = Intersect(e_1, m)
A1 = NaN
h_1 = Circle(I, Distance[E, A_1] / (1 + (a * h)))
B_1, C_1 = Intersect(h_1, n)
k_1 = Circle(B, Distance[I, C_1] / (1 + (a * h)))
D_1, E_1 = Intersect(k_1, p)
b = Segment(L, N)
i_1 = Segment(N, P)
j_1 = Segment(P, R)
l_1 = Segment(R, U)
m_1 = Segment(U, W)
n_1 = Segment(W, A_1)
p_1 = Segment(A_1, C_1)
q_1 = Segment(C_1, E_1)
r_1 = Line(N, xAxis)
s_1 = Line(P, xAxis)
t_1 = Line(R, xAxis)
a_1 = Line(U, xAxis)
b_1 = Line(W, xAxis)
f_2 = Line(A_1, xAxis)
g_2 = Line(C_1, f)
h_2 = Line(E_1, f)
F_1 = Intersect(f_1, r_1, (0.9162907319059133, 0.39999999998729674))
i_2 = Tangent(F_1, f_1)
G_1 = Intersect(f_1, s_1, (1.8325814654353227, 0.159999999730078))
j_2 = Tangent(G_1, f_1)
H_1 = Intersect(f_1, t_1, (2.748872195622468, 0.06399999999999983))
k_2 = Tangent(H_1, f_1)
I_1 = Intersect(f_1, a_1, (3.6651629274950457, 0.025600000000040313))
l_2 = Tangent(I_1, f_1)
J_1 = Intersect(f_1, b_1, (4.581453659375437, 0.01023999999995227))
m_2 = Tangent(J_1, f_1)
K_1 = Intersect(f_1, f_2, (5.497744391149999, 0.0040960000003888416))
n_2 = Tangent(K_1, f_1)
L_1 = Intersect(f_1, h_2, (7.330325846763363, 0.000655360005393533))
M_1 = Intersect(g_2, h_2)
p_2 = Tangent(H_1, f_1)