4.35.7 $a^{2}y(x)+x^4{y}^{″}(x)=0$

ODE
$$a^{2}y(x)+x^4{y}^{″}(x)=0$$ ODE Classification

[[_Emden, _Fowler]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0665238 (sec), leaf count = 57

$$\left\{\{y(x)\to c_{1}x{e}^{\frac{\sqrt{-a^2}}{x}}+\frac{c_{2}x{e}^{-\frac{\sqrt{-a^2}}{x}}}{2\sqrt{-a^2}}\}\right\}$$

Maple ✓
cpu = 0.033 (sec), leaf count = 23

$$\{y\left(x\right)=x(\cos \left(\frac{a}{x}\right)\mathit{\_}\mathit{C}\mathit{2}+\sin \left(\frac{a}{x}\right)\mathit{\_}\mathit{C}\mathit{1})\}$$ Mathematica raw input

DSolve[a^2*y[x] + x^4*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> E^(Sqrt[-a^2]/x)*x*C[1] + (x*C[2])/(2*Sqrt[-a^2]*E^(Sqrt[-a^2]/x))}}

Maple raw input

dsolve(x^4*diff(diff(y(x),x),x)+a^2*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = x*(cos(1/x*a)*_C2+sin(1/x*a)*_C1)