\[ c y(x) \sqrt [5]{a x+b}+5 (a x+b) y''(x)+8 a y'(x)=0 \] ✓ Mathematica : cpu = 0.0373262 (sec), leaf count = 108
\[\left \{\left \{y(x)\to \frac {6 a c_1 \cos \left (\frac {\sqrt {5} \sqrt {c} (a x+b)^{3/5}}{3 a}\right )}{\sqrt {5} \sqrt {c} (a x+b)^{3/5}}+\frac {3 a c_2 \sin \left (\frac {\sqrt {5} \sqrt {c} (a x+b)^{3/5}}{3 a}\right )}{\sqrt {5} \sqrt {c} (a x+b)^{3/5}}\right \}\right \}\] ✓ Maple : cpu = 0.885 (sec), leaf count = 53
\[ \left \{ y \left ( x \right ) ={ \left ( {\it \_C2}\,\cosh \left ( {\frac {1}{3\,a} \left ( ax+b \right ) ^{{\frac {3}{5}}}\sqrt {-5\,c}} \right ) +{\it \_C1}\,\sinh \left ( {\frac {1}{3\,a} \left ( ax+b \right ) ^{{\frac {3}{5}}}\sqrt {-5\,c}} \right ) \right ) \left ( ax+b \right ) ^{-{\frac {3}{5}}}} \right \} \]