Euler-Lagrange Acceleration

Problem

For the Lagrangian density F(y, y', x) = a*y'^2 + b*y^2 + c*y*x, the Euler-Lagrange equation requires the x-derivative of 2*a*y' to equal 2*b*y + c*x.

Solving for the acceleration gives y'' = (2*b*y + c*x) / (2*a). Given a != 0, b, c, the current value y, and the coordinate x, return y''.

Hint

The Euler-Lagrange equation balances d/dx of the momentum against the force term.

Test cases

case 1

in: [1,0,0,5,3]

expected: 0

case 2

in: [1,1,0,2,0]

expected: 2

case 3

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

expected: 2

case 4

in: [1,0,4,0,1]

expected: 2

Starter codePython

def euler_lagrange_acceleration(a, b, c, y, x):
    # Your code here
    pass

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