MediumCalculusca-125

Exact ODE Potential

Problem

The differential M(x, y) dx + N(x, y) dy = 0 with M = a*x + b*y and N = c*x + d*y is exact exactly when b == c.

When it is exact, return the potential phi(x, y) = 0.5*a*x^2 + b*x*y + 0.5*d*y^2 with phi(0, 0) = 0. Otherwise return None.

Hint

Exactness requires the cross partials to match: dM/dy = dN/dx.

case 1

in: [1,1,1,1,2,3]

expected: 12.5

case 2

in: [2,-3,-3,4,1,1]

expected: 0

case 3

in: [1,2,3,4,1,1]

expected: null

case 4

in: [0,0,0,0,5,5]

expected: 0

Starter codePython

def exact_ode_potential(a, b, c, d, x, y):
    # Return None when the equation is not exact
    # Your code here
    pass

4 test cases · run your code against them in the editor