ODE
\[ x^{3/2} y''(x)=f\left (\frac {y(x)}{\sqrt {x}}\right ) \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 600.311 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.199 (sec), leaf count = 84
\[ \left \{ {\frac {\ln \left ( x \right ) }{2}}-\int ^{{y \left ( x \right ) {\frac {1}{\sqrt {x}}}}}\!{\frac {1}{\sqrt {{\it \_C1}+8\,\int \!f \left ( {\it \_g} \right ) \,{\rm d}{\it \_g}+{{\it \_g}}^{2}}}}{d{\it \_g}}-{\it \_C2}=0,{\frac {\ln \left ( x \right ) }{2}}+\int ^{{y \left ( x \right ) {\frac {1}{\sqrt {x}}}}}\!{\frac {1}{\sqrt {{\it \_C1}+8\,\int \!f \left ( {\it \_g} \right ) \,{\rm d}{\it \_g}+{{\it \_g}}^{2}}}}{d{\it \_g}}-{\it \_C2}=0,y \left ( x \right ) ={\it RootOf} \left ( 4\,f \left ( {\frac {{\it \_Z}}{\sqrt {x}}} \right ) \sqrt {x}+{\it \_Z} \right ) \right \} \] Mathematica raw input
DSolve[x^(3/2)*y''[x] == f[y[x]/Sqrt[x]],y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(x^(3/2)*diff(diff(y(x),x),x) = f(y(x)/x^(1/2)), y(x),'implicit')
Maple raw output
y(x) = RootOf(4*f(_Z/x^(1/2))*x^(1/2)+_Z), 1/2*ln(x)-Intat(1/(_C1+8*Int(f(_g),_g)+_g^2)^(1/2),_g = y(x)/x^(1/2))-_C2 = 0, 1/2*ln(x)+Intat(1/(_C1+8*Int(f(_g),_g)+_g^2)^(1/2),_g = y(x)/x^(1/2))-_C2 = 0