Find (gamma) so that the solution of the initial value problem
has finite limit as x → 0.
I'm not sure I fully understand the problem. I can solve the homogeneous equation using the indicial equation, letting y = x^r:
r^2 - r - 20 = 0
r= -4 , 5
y=c1 * x^-4 + c2 * x^5
for y(1)=1, 1 = c1 + c2 => c1 = 1- c2
for y'(1) = gamma, gamma = -4c1 + 5c2 => gamma = -4 + 4c2 + 5c2
c1 = (-gamma/9 + 5/9)
c2 = (gamma + 4)/9
thus y= (-gamma/9 + 5/9)x^-4 + ((gamma + 4)/9)x^5
but that doesn't seem to address the bit about the finite limit of the gamma function.... and my prof wants the answer in "gamma =" .......