ODE
\[ a y(x)+x^2 y''(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.167667 (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
\[\left [y \left (x \right ) = \textit {\_C1} \,x^{\frac {\sqrt {1-4 a}}{2}+\frac {1}{2}}+\textit {\_C2} \,x^{\frac {1}{2}-\frac {\sqrt {1-4 a}}{2}}\right ]\] 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))
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))]