4.30.32 $x^2{y}^{″}(x)+5x{y}^{\prime }(x)+13y(x)=0$

ODE
$$x^2{y}^{″}(x)+5x{y}^{\prime }(x)+13y(x)=0$$ ODE Classification

[[_Emden, _Fowler]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0112846 (sec), leaf count = 26

$$\left\{\{y(x)\to \frac{c_1\sin (3\log (x))+c_2\cos (3\log (x))}{x^2}\}\right\}$$

Maple ✓
cpu = 0.005 (sec), leaf count = 23

$$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}\sin (3\ln \left(x\right))+\mathit{\_}\mathit{C}\mathit{2}\cos (3\ln \left(x\right))}{x^2}\}$$ 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