Find all the solutions of the second-order differential equations. When an initial condition is given, find the particular solution satisfying that condition.

a. \(y^{\prime \prime}-9 y^{\prime}+20 y=0\).

b. \(y^{\prime \prime}-3 y^{\prime}+4 y=0, \quad y(0)=0, \quad y^{\prime}(0)=1\).

c. \(x^{2} y^{\prime \prime}+5 x y^{\prime}+4 y=0, \quad x>0\).

d. \(x^{2} y^{\prime \prime}-2 x y^{\prime}+3 y=0, \quad x>0\).