The solution to Legendre's linear differential equation
(3x + 2)2\(\frac{d^{2}y}{dx^{2}}\) + 3(3x + 2)\(\frac{dy}{dx}\) − 36y = 3x2 + 4x + 1 is:
1
y = C1(3x − 2)2 + C2(3x + 2)−2 −\(\frac{1}{108}\)[(3x + 2)2 log(3x + 2) + 1]
2
y = C1(3x − 2)2 + C2(3x + 2)−2 + \(\frac{1}{108}\)[(3x + 2)2 log(3x + 2) + 1]
3
y = C1(3x + 2)2 + C2(3x + 2)−2 + \(\frac{1}{108}\)[(3x + 2)2 log(3x + 2) + 1]
4
y = C1(3x + 2)2 + C2(3x + 2)−2 − \(\frac{1}{108}\)[(3x + 2)2 log(3x + 2) + 1]
5
Not Attempted