ODE
\[ x^2 y''(x)+5 x y'(x)+13 y(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0112846 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {c_1 \sin (3 \log (x))+c_2 \cos (3 \log (x))}{x^2}\right \}\right \}\]
Maple ✓
cpu = 0.005 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,\sin \left ( 3\,\ln \left ( x \right ) \right ) +{\it \_C2}\,\cos \left ( 3\,\ln \left ( x \right ) \right ) }{{x}^{2}}} \right \} \] Mathematica raw input
DSolve[13*y[x] + 5*x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[2]*Cos[3*Log[x]] + C[1]*Sin[3*Log[x]])/x^2}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+13*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C1*sin(3*ln(x))+_C2*cos(3*ln(x)))/x^2