\[ (x-a)^5 (x-b)^5 y^{(5)}(x)-c y(x)=0 \] ✓ Mathematica : cpu = 270.838 (sec), leaf count = 331
DSolve[-(c*y[x]) + (-a + x)^5*(-b + x)^5*Derivative[5][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 (x-b)^4 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^5+10 \text {$\#$1}^4-35 \text {$\#$1}^3+50 \text {$\#$1}^2-24 \text {$\#$1}+\frac {c}{(a-b)^5}\& ,1\right ]}+c_2 (x-b)^4 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^5+10 \text {$\#$1}^4-35 \text {$\#$1}^3+50 \text {$\#$1}^2-24 \text {$\#$1}+\frac {c}{(a-b)^5}\& ,2\right ]}+c_3 (x-b)^4 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^5+10 \text {$\#$1}^4-35 \text {$\#$1}^3+50 \text {$\#$1}^2-24 \text {$\#$1}+\frac {c}{(a-b)^5}\& ,3\right ]}+c_4 (x-b)^4 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^5+10 \text {$\#$1}^4-35 \text {$\#$1}^3+50 \text {$\#$1}^2-24 \text {$\#$1}+\frac {c}{(a-b)^5}\& ,4\right ]}+c_5 (x-b)^4 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^5+10 \text {$\#$1}^4-35 \text {$\#$1}^3+50 \text {$\#$1}^2-24 \text {$\#$1}+\frac {c}{(a-b)^5}\& ,5\right ]}\right \}\right \}\] ✗ Maple : cpu = 0. (sec), leaf count = 0
dsolve((x-a)^5*(x-b)^5*diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-c*y(x)=0,y(x))
, result contains DESol or ODESolStruc
\[\text {Expression too large to display}\]