4.45.49 $5y^{‴}(x)+x{y}^{⁗}(x)=0$

ODE
$$5y^{‴}(x)+x{y}^{⁗}(x)=0$$ ODE Classification

[[_high_order, _missing_y]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.00903929 (sec), leaf count = 27

$$\left\{\{y(x)\to c_4{x}^2-\frac{c_1}{24x^2}+c_{3}x+c_2\}\right\}$$

Maple ✓
cpu = 0.011 (sec), leaf count = 19

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{C}\mathit{2}x+\mathit{\_}\mathit{C}\mathit{3}{x}^2+\frac{\mathit{\_}\mathit{C}\mathit{4}}{x^2}\}$$ Mathematica raw input

DSolve[5*y'''[x] + x*y''''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -C[1]/(24*x^2) + C[2] + x*C[3] + x^2*C[4]}}

Maple raw input

dsolve(x*diff(diff(diff(diff(y(x),x),x),x),x)+5*diff(diff(diff(y(x),x),x),x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1+_C2*x+_C3*x^2+_C4/x^2