MediumCalculusca-126

Nonhomogeneous Particular Solution

Problem

For the ODE y'' + p*y' + q*y = A*e^(r*x), a particular solution has the form y_p = A*e^(r*x) / (r^2 + p*r + q), provided the denominator is nonzero (no resonance).

Given p, q, A, r, and the evaluation point x, return y_p(x). If r^2 + p*r + q == 0, return None.

Hint

Substitute the exponential guess into the ODE and solve for the constant.

Test cases

case 1

in: [3,2,1,1,0]

expected: 0.16666666666666666

case 2

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

expected: 2

case 3

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

expected: 1

case 4

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

expected: 0.45304697140984085

case 5

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

expected: null

Starter codePython

def particular_solution_value(p, q, big_a, r, x):
    # Return None on resonance
    # Your code here
    pass

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