ODE
\[ \text {a1} x y'(x)+\text {a2} y(x)+x^2 y''(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.159659 (sec), leaf count = 57
\[\left \{\left \{y(x)\to x^{\frac {1}{2} \left (-\sqrt {\text {a1}^2-2 \text {a1}-4 \text {a2}+1}-\text {a1}+1\right )} \left (c_2 x^{\sqrt {\text {a1}^2-2 \text {a1}-4 \text {a2}+1}}+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.036 (sec), leaf count = 53
\[\left [y \left (x \right ) = \textit {\_C1} \,x^{-\frac {\mathit {a1}}{2}+\frac {1}{2}+\frac {\sqrt {\mathit {a1}^{2}-2 \mathit {a1} -4 \mathit {a2} +1}}{2}}+\textit {\_C2} \,x^{-\frac {\mathit {a1}}{2}+\frac {1}{2}-\frac {\sqrt {\mathit {a1}^{2}-2 \mathit {a1} -4 \mathit {a2} +1}}{2}}\right ]\] Mathematica raw input
DSolve[a2*y[x] + a1*x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x^((1 - a1 - Sqrt[1 - 2*a1 + a1^2 - 4*a2])/2)*(C[1] + x^Sqrt[1 - 2*a1 + a1^2 - 4*a2]*C[2])}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+a1*x*diff(y(x),x)+a2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^(-1/2*a1+1/2+1/2*(a1^2-2*a1-4*a2+1)^(1/2))+_C2*x^(-1/2*a1+1/2-1/2*(a1^2-2*a1-4*a2+1)^(1/2))]