DSolve[{[CurlyEpsilon] fB +
D[y[fB, a], {fB, 1}]/
 y[fB, a] ([CurlyEpsilon] [Gamma]B - c (fB - fbar)) +
1/2 [CurlyEpsilon] ([CurlyEpsilon] - 1) sD^2 +
1/2 D[y[fB, a], {fB, 2}]/y[fB, a] [Gamma]B^2 (1/sD^2 + 1/sS^2) -
D[y[fB, a], {a, 1}]/y[fB, a] == 0, y[fB, 0] == 1}, y[fB, a], {fB, a}]

ySol[fB_, a_] := Exp[[CurlyEpsilon] (fbar (a) - 1/c (fB - fbar) (E^(-c a) - 1)) +
1/2 [CurlyEpsilon]^2 ([Gamma]B^2/sD^2 + [Gamma]B^2/
   sS^2) (1/c^2 a + 1/c^3 (E^(-c a) - 1) -
   1/2 1/c^3 (E^(-c a) - 1)^2) +
1/2 [CurlyEpsilon] ([CurlyEpsilon] -
   1) sD^2 a + [CurlyEpsilon]^2 [Gamma]B/
 c (a + 1/c (E^(-c a) - 1))];

D[ySol[fB, a], {fB, 1}]/ ySol[fB, a] == -(((-1 + E^(-a c)) [CurlyEpsilon])/c)

D[ySol[fB, a], {fB, 2}]/ ySol[fB, a] == ((-1 + E^(-a c))^2 [CurlyEpsilon]^2)/c^2

Integrate[[CurlyEpsilon] fB - ((-1 + E^(-c (a))) [CurlyEpsilon])/   c ([CurlyEpsilon] [Gamma]B - c (fB - fbar)) +   1/2 [CurlyEpsilon] ([CurlyEpsilon] - 1) sD^2 +   1/2 ((-1 + E^(-c (a)))^2 [CurlyEpsilon]^2)/   c^2 [Gamma]B^2 (1/sD^2 + 1/sS^2), a]

Temp[a_, fB_] :=  Exp[1/2 [CurlyEpsilon] (a (2 fbar +
     sD^2 (-1 + [CurlyEpsilon])) + (
  E^(-2 a c) (-1 + 4 E^(a c)) (sD^2 +
     sS^2) [Gamma]B^2 [CurlyEpsilon])/(
  2 c^3 sD^2 sS^2) + ([Gamma]B (2 E^(-a c) +
     a (1/sD^2 + 1/sS^2) [Gamma]B) [CurlyEpsilon])/c^2 + (
  2 E^(-a c) (-fB + fbar + a E^(a c) [Gamma]B [CurlyEpsilon]))/
  c)];

D[Temp[a, fB], {fB, 1}]/Temp[a, fB] == -((E^(-a c) [CurlyEpsilon])/c)