ODE
\[ a y(x)+x^2 y''(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00973846 (sec), leaf count = 42
\[\left \{\left \{y(x)\to x^{\frac {1}{2}-\frac {1}{2} \sqrt {1-4 a}} \left (c_2 x^{\sqrt {1-4 a}}+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{{\frac {1}{2}\sqrt {1-4\,a}}+{\frac {1}{2}}}+{\it \_C2}\,{x}^{{\frac {1}{2}}-{\frac {1}{2}\sqrt {1-4\,a}}} \right \} \] Mathematica raw input
DSolve[a*y[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x^(1/2 - Sqrt[1 - 4*a]/2)*(C[1] + x^Sqrt[1 - 4*a]*C[2])}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+a*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*x^(1/2*(1-4*a)^(1/2)+1/2)+_C2*x^(1/2-1/2*(1-4*a)^(1/2))