\[ (x-a)^3 (x-b)^3 y^{(3)}(x)-c y(x)=0 \] ✓ Mathematica : cpu = 130.096 (sec), leaf count = 165
DSolve[-(c*y[x]) + (-a + x)^3*(-b + x)^3*Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 (x-b)^2 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^3+3 \text {$\#$1}^2-2 \text {$\#$1}+\frac {c}{(a-b)^3}\& ,1\right ]}+c_2 (x-b)^2 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^3+3 \text {$\#$1}^2-2 \text {$\#$1}+\frac {c}{(a-b)^3}\& ,2\right ]}+c_3 (x-b)^2 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^3+3 \text {$\#$1}^2-2 \text {$\#$1}+\frac {c}{(a-b)^3}\& ,3\right ]}\right \}\right \}\] ✓ Maple : cpu = 0.5 (sec), leaf count = 437
dsolve((x-a)^3*(x-b)^3*diff(diff(diff(y(x),x),x),x)-y(x)*c=0,y(x))
\[y \left (x \right ) = \left (x -a \right )^{-\frac {2 b}{a -b}} \left (x -b \right )^{\frac {2 a}{a -b}} \left (\left (b -x \right )^{-\frac {\operatorname {RootOf}\left (\textit {\_Z}^{3}+\left (-3 a -3 b \right ) \textit {\_Z}^{2}+\left (2 a^{2}+8 a b +2 b^{2}\right ) \textit {\_Z} -4 a^{2} b -4 a \,b^{2}-c , \operatorname {index} =3\right )}{a -b}} \left (a -x \right )^{\frac {\operatorname {RootOf}\left (\textit {\_Z}^{3}+\left (-3 a -3 b \right ) \textit {\_Z}^{2}+\left (2 a^{2}+8 a b +2 b^{2}\right ) \textit {\_Z} -4 a^{2} b -4 a \,b^{2}-c , \operatorname {index} =3\right )}{a -b}} c_{3}+\left (b -x \right )^{-\frac {\operatorname {RootOf}\left (\textit {\_Z}^{3}+\left (-3 a -3 b \right ) \textit {\_Z}^{2}+\left (2 a^{2}+8 a b +2 b^{2}\right ) \textit {\_Z} -4 a^{2} b -4 a \,b^{2}-c , \operatorname {index} =2\right )}{a -b}} \left (a -x \right )^{\frac {\operatorname {RootOf}\left (\textit {\_Z}^{3}+\left (-3 a -3 b \right ) \textit {\_Z}^{2}+\left (2 a^{2}+8 a b +2 b^{2}\right ) \textit {\_Z} -4 a^{2} b -4 a \,b^{2}-c , \operatorname {index} =2\right )}{a -b}} c_{2}+\left (b -x \right )^{-\frac {\operatorname {RootOf}\left (\textit {\_Z}^{3}+\left (-3 a -3 b \right ) \textit {\_Z}^{2}+\left (2 a^{2}+8 a b +2 b^{2}\right ) \textit {\_Z} -4 a^{2} b -4 a \,b^{2}-c , \operatorname {index} =1\right )}{a -b}} \left (a -x \right )^{\frac {\operatorname {RootOf}\left (\textit {\_Z}^{3}+\left (-3 a -3 b \right ) \textit {\_Z}^{2}+\left (2 a^{2}+8 a b +2 b^{2}\right ) \textit {\_Z} -4 a^{2} b -4 a \,b^{2}-c , \operatorname {index} =1\right )}{a -b}} c_{1}\right )\]