4.44.9 $x{y}^{‴}(x)-y^{″}(x)-x{y}^{\prime }(x)+y(x)=0$

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

[[_3rd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0575287 (sec), leaf count = 24

$$\left\{\{y(x)\to c_{1}x+i{c}_3\sinh (x)-c_2\cosh (x)\}\right\}$$

Maple ✓
cpu = 0.087 (sec), leaf count = 18

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

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

Mathematica raw output

{{y[x] -> x*C[1] - C[2]*Cosh[x] + I*C[3]*Sinh[x]}}

Maple raw input

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

Maple raw output

y(x) = _C1*x+_C2*exp(x)+_C3*exp(-x)