ES1 - Case A (one plane)
f = x
x' = fy
y' = fz
z' = f(-x + ay^2 - xz)
a = 1.54
IC = (6, 0, -1)  <-- NOTE CHANGE
LE = (0.0071, 0, -1.0869)
Dky = 2.0065

ES2 - Case F (one plane)
f = x
x' = fy
y' = f(-x + az)
z' = f(by^2 - xz)
a = 1, b = 3
IC = (0.15, 0, 0.8)
LE = (0.0644, 0, -0.8279)
Dky = 2.0778

ES3 - Case G (one plane)
f = x
x' = f(y^2 + axy)
y' = -fz
z' = f(b + xy)
a = 2, b = 1
IC = (0.87, 0.4, 0)
LE = (0.0661, 0, -1.6644)
Dky = 2.0397

ES4 - Case I (two planes)
f = xy
x' = -faz
y' = f(b + z^2 - xy)
z' = f(x^2 - xy)
a = 0.4, b = 1
IC = (1, 1.44, 0)  <-- NOTE CHANGE
LE = (0.1242, 0, -1.8356)
Dky = 2.0677

ES5 - Case J (three planes)  <-- NOTE CHANGES
f = xyz
x' = f(y + ayz)
y' = f(bz + y^2 + cz^2)
z' = f(x^2 - y^2)
a = 2, b = 8, c = 7
IC = (1, -1.3, -1)
LE = (0.0294, 0, -0.4051)
Dky = 2.0725

ES6 - Case D (sphere)
f = 1 - x^2 - y^2 - z^2
x' = fay
y' = fxz
z' = -f(z + x^2 + byz)
a = 0.4, b = 6
IC = (0, 0.1, 0)
LE = (0.0113, 0, -0.9501)
Dky = 2.0119

ES7 - Case H (sphere)
f = 1 - x^2 - y^2 - z^2
x' = f(az + y^2)
y' = f(-y + bx^2)
z' = -fxy
a = 1, b = 5
IC = (0.24, 0.2, 0)
LE = (0.0323, 0, -0.9552)
Dky = 2.0338

ES8 - Case B (circular cylinder)
f = 1 - x^2 - y^2
x' = f(y^2 - axy)
y' = fxz
z' = f(1 - by^2)
a = 5, b = 7
IC = (0.06, 0, 1)
LE = (0.0388, 0, -1.2078)
Dky = 2.0321

ES9 - Case C (hyperbolic cylinder)
f = 1 + x^2 - y^2
x' = f(a - z^2)
y' = fxz
z' = f(y + bxz)
a = 0.1, b = 1
IC = (0, -0.08, 0)
LE = (0.0420, 0, -0.2230)
Dky = 2.1883

ES10 - Case E (paraboloid)
f = z + x^2 + y^2
x' = f*yz
y' = f*(x - axz)
z' = f*(x - bz^2)
a = 1, b = 0.6
IC = (0.46, 0, 0.8)
LE = (0.0283, 0, -0.6171) 
Dky = 2.0458

ES11 - Case K (saddle)
f = z + x^2 - y^2
x' = fyz
y' = -fax 
z' = f(-z + by^2 + xz)
a = 0.1, b = 6
IC = (1, 0, 1)
LE = (0.0068, 0, -0.4998)
Dky = 2.0135

ES12 - Case L (one plane)
f = z
x' = -fy
y' = -fxz 
z' = f(ay^2 + xz - b)
a = 2, b = 0.35
IC = (0, 0.4, 1)
LE = (0.0562, 0, -1.0860)
Dky = 2.051