\[ y(x) \left (a (a+b)+b^2 c^2 x^{2 b}\right )-x (2 a+b-1) y'(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0330901 (sec), leaf count = 106
DSolve[(a*(a + b) + b^2*c^2*x^(2*b))*y[x] - (-1 + 2*a + b)*x*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 2^{-\frac {a}{b}} c^{a/b} \left (x^{2 b}\right )^{\frac {a}{2 b}} \cos \left (c \sqrt {x^{2 b}}\right )+c_2 2^{-\frac {a+b}{b}} c^{\frac {a+b}{b}-1} \left (x^{2 b}\right )^{\frac {a+b}{2 b}-\frac {1}{2}} \sin \left (c \sqrt {x^{2 b}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.089 (sec), leaf count = 25
dsolve(x^2*diff(diff(y(x),x),x)-(2*a+b-1)*x*diff(y(x),x)+(c^2*b^2*x^(2*b)+a*(a+b))*y(x)=0,y(x))
\[y \left (x \right ) = x^{a} \left (\sin \left (x^{b} c \right ) c_{1}+\cos \left (x^{b} c \right ) c_{2}\right )\]