4.45.1 $4x^3{y}^{‴}(x)+x{y}^{\prime }(x)-y(x)=0$

ODE
$$4x^3{y}^{‴}(x)+x{y}^{\prime }(x)-y(x)=0$$ ODE Classification

[[_3rd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0133121 (sec), leaf count = 38

$$\left\{\{y(x)\to x(c_1{x}^{-\frac{\sqrt{3}}{2}}+c_2{x}^{\frac{\sqrt{3}}{2}}+c_3)\}\right\}$$

Maple ✓
cpu = 0.007 (sec), leaf count = 30

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

DSolve[-y[x] + x*y'[x] + 4*x^3*y'''[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(4*x^3*diff(diff(diff(y(x),x),x),x)+x*diff(y(x),x)-y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*x+_C2*x^(1+1/2*3^(1/2))+_C3*x^(1-1/2*3^(1/2))