ODE
\[ x y'(x) \left (\text {a0}+\text {a1} x^r+\text {a2} x^s\right )+y(x) \left (\text {b0}+\text {b1} x^r+\text {b2} x^{2 r}+\text {b3} x^s+\text {b4} x^{2 s}+\text {b5} x^{r+s}\right )+x^2 y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 2.40625 (sec), leaf count = 0 , could not solve
DSolve[(b0 + b1*x^r + b2*x^(2*r) + b3*x^s + b4*x^(2*s) + b5*x^(r + s))*y[x] + x*(a0 + a1*x^r + a2*x^s)*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0, y[x], x]
Maple ✗
cpu = 2.178 (sec), leaf count = 0 , result contains DESol
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +{\frac { \left ( {\it a0}+{\it a1}\,{x}^{r}+{\it a2}\,{x}^{s} \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) }{x}}+{\frac { \left ( {\it b0}+{\it b1}\,{x}^{r}+{\it b2}\,{x}^{2\,r}+{\it b3}\,{x}^{s}+{\it b4}\,{x}^{2\,s}+{\it b5}\,{x}^{r+s} \right ) {\it \_Y} \left ( x \right ) }{{x}^{2}}} \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]
Mathematica raw input
DSolve[(b0 + b1*x^r + b2*x^(2*r) + b3*x^s + b4*x^(2*s) + b5*x^(r + s))*y[x] + x*(a0 + a1*x^r + a2*x^s)*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[(b0 + b1*x^r + b2*x^(2*r) + b3*x^s + b4*x^(2*s) + b5*x^(r + s))*y[x] + x*(a0 + a1*x^r + a2*x^s)*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x*(a0+a1*x^r+a2*x^s)*diff(y(x),x)+(b0+b1*x^r+b2*x^(2*r)+b3*x^s+b4*x^(2*s)+b5*x^(r+s))*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = DESol({diff(diff(_Y(x),x),x)+1/x*(a0+a1*x^r+a2*x^s)*diff(_Y(x),x)+(b0+b1*x^r+b2*x^(2*r)+b3*x^s+b4*x^(2*s)+b5*x^(r+s))/x^2*_Y(x)},{_Y(x)})