\[ (2 a x+b) y'(x)+a y(x)+2 (x-1) x y^{(3)}(x)+3 (2 x-1) y''(x)=0 \] ✓ Mathematica : cpu = 60.2859 (sec), leaf count = 115
DSolve[a*y[x] + (b + 2*a*x)*Derivative[1][y][x] + 3*(-1 + 2*x)*Derivative[2][y][x] + 2*(-1 + x)*x*Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_3 \text {MathieuC}\left [-\frac {a}{2}-\frac {b}{2}+1,\frac {a}{4},\cos ^{-1}\left (\sqrt {x}\right )\right ] \text {MathieuS}\left [-\frac {a}{2}-\frac {b}{2}+1,\frac {a}{4},\cos ^{-1}\left (\sqrt {x}\right )\right ]+c_1 \text {MathieuC}\left [-\frac {a}{2}-\frac {b}{2}+1,\frac {a}{4},\cos ^{-1}\left (\sqrt {x}\right )\right ]^2+c_2 \text {MathieuS}\left [-\frac {a}{2}-\frac {b}{2}+1,\frac {a}{4},\cos ^{-1}\left (\sqrt {x}\right )\right ]^2\right \}\right \}\] ✓ Maple : cpu = 0.144 (sec), leaf count = 79
dsolve(2*x*(x-1)*diff(diff(diff(y(x),x),x),x)+3*(2*x-1)*diff(diff(y(x),x),x)+(2*a*x+b)*diff(y(x),x)+a*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \MathieuC \left (-\frac {a}{2}-\frac {b}{2}+1, \frac {a}{4}, \arccos \left (\sqrt {x}\right )\right )^{2}+c_{2} \MathieuS \left (-\frac {a}{2}-\frac {b}{2}+1, \frac {a}{4}, \arccos \left (\sqrt {x}\right )\right )^{2}+c_{3} \MathieuC \left (-\frac {a}{2}-\frac {b}{2}+1, \frac {a}{4}, \arccos \left (\sqrt {x}\right )\right ) \MathieuS \left (-\frac {a}{2}-\frac {b}{2}+1, \frac {a}{4}, \arccos \left (\sqrt {x}\right )\right )\]