\[ c y(x) \sqrt [5]{a x+b}+5 (a x+b) y''(x)+8 a y'(x)=0 \] ✓ Mathematica : cpu = 0.0342383 (sec), leaf count = 108
DSolve[c*(b + a*x)^(1/5)*y[x] + 8*a*Derivative[1][y][x] + 5*(b + a*x)*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {6 a c_1 \cos \left (\frac {\sqrt {5} \sqrt {c} (a x+b)^{3/5}}{3 a}\right )}{\sqrt {5} \sqrt {c} (a x+b)^{3/5}}+\frac {3 a c_2 \sin \left (\frac {\sqrt {5} \sqrt {c} (a x+b)^{3/5}}{3 a}\right )}{\sqrt {5} \sqrt {c} (a x+b)^{3/5}}\right \}\right \}\] ✓ Maple : cpu = 0.102 (sec), leaf count = 53
dsolve(5*(a*x+b)*diff(diff(y(x),x),x)+8*a*diff(y(x),x)+c*(a*x+b)^(1/5)*y(x)=0,y(x))
\[y \left (x \right ) = \frac {c_{2} \cosh \left (\frac {\left (a x +b \right )^{\frac {3}{5}} \sqrt {-5 c}}{3 a}\right )+c_{1} \sinh \left (\frac {\left (a x +b \right )^{\frac {3}{5}} \sqrt {-5 c}}{3 a}\right )}{\left (a x +b \right )^{\frac {3}{5}}}\]