How can we derivate a implicit equation in Python 3?
Example x^2+y^2=25 differentiation is: dy/dx=-x/y, when try this:
from sympy import *
init_printing(use_unicode=True)
x = symbols('x')
y = Function('y')(x)
eq = x**2+y**2-25
sol = diff(eq, x)
print(sol)
But it shows:
2*x + 2*y(x)*Derivative(y(x), x)
How can get -x/y?
SymPy has the function idiff which does what you want
In [2]: idiff(x**2+y**2-25, y, x)
Out[2]:
-x
───
y
You may use the implicit function theorem which states that when two variables x, y, are related by the implicit equation f(x, y) = 0, then the derivative of y with respect to x is equal to - (df/dx) / (df/dy) (as long as the partial derivatives are continuous and df/dy != 0).
x, y = symbols('x, y')
f = x**2 + y**2 - 25
-diff(f,x)/diff(f,y)
-x/y
You have the differential equation, so you can rearrange it using solve:
solve(sol, diff(y, x, 1))
