4.45.42 $-3y^{‴}(x)+y^{⁗}(x)+y^{″}(x)-y^{\prime }(x)=0$

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

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0394146 (sec), leaf count = 143

$$\left\{\{y(x)\to \frac{c_1{e}^{x\text{Root}[{\mathrm{\#}\text{1}}^3-3{\mathrm{\#}\text{1}}^2+\mathrm{\#}\text{1}-1\mathrm{\&},1]}}{\text{Root}[{\mathrm{\#}\text{1}}^3-3{\mathrm{\#}\text{1}}^2+\mathrm{\#}\text{1}-1\mathrm{\&},1]}+\frac{c_3{e}^{x\text{Root}[{\mathrm{\#}\text{1}}^3-3{\mathrm{\#}\text{1}}^2+\mathrm{\#}\text{1}-1\mathrm{\&},3]}}{\text{Root}[{\mathrm{\#}\text{1}}^3-3{\mathrm{\#}\text{1}}^2+\mathrm{\#}\text{1}-1\mathrm{\&},3]}+\frac{c_2{e}^{x\text{Root}[{\mathrm{\#}\text{1}}^3-3{\mathrm{\#}\text{1}}^2+\mathrm{\#}\text{1}-1\mathrm{\&},2]}}{\text{Root}[{\mathrm{\#}\text{1}}^3-3{\mathrm{\#}\text{1}}^2+\mathrm{\#}\text{1}-1\mathrm{\&},2]}+c_4\}\right\}$$

Maple ✓
cpu = 0.035 (sec), leaf count = 172

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\frac{({(27+3\sqrt{57})}^{\frac{2}{3}}+3\sqrt[3]{27+3\sqrt{57}}+6)x}{3\sqrt[3]{27+3\sqrt{57}}}}-\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{-\frac{({(27+3\sqrt{57})}^{\frac{2}{3}}-6\sqrt[3]{27+3\sqrt{57}}+6)x}{6\sqrt[3]{27+3\sqrt{57}}}}\sin \left(\frac{\sqrt{3}({(27+3\sqrt{57})}^{\frac{2}{3}}-6)x}{6\sqrt[3]{27+3\sqrt{57}}}\right)+\mathit{\_}\mathit{C}\mathit{4}{\mathrm{e}}^{-\frac{({(27+3\sqrt{57})}^{\frac{2}{3}}-6\sqrt[3]{27+3\sqrt{57}}+6)x}{6\sqrt[3]{27+3\sqrt{57}}}}\cos \left(\frac{\sqrt{3}({(27+3\sqrt{57})}^{\frac{2}{3}}-6)x}{6\sqrt[3]{27+3\sqrt{57}}}\right)\}$$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> C[4] + (E^(x*Root[-1 + #1 - 3*#1^2 + #1^3 & , 1, 0])*C[1])/Root[-1 + #
1 - 3*#1^2 + #1^3 & , 1, 0] + (E^(x*Root[-1 + #1 - 3*#1^2 + #1^3 & , 2, 0])*C[2]
)/Root[-1 + #1 - 3*#1^2 + #1^3 & , 2, 0] + (E^(x*Root[-1 + #1 - 3*#1^2 + #1^3 & 
, 3, 0])*C[3])/Root[-1 + #1 - 3*#1^2 + #1^3 & , 3, 0]}}

Maple raw input

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

Maple raw output

y(x) = _C1+_C2*exp(1/3*((27+3*57^(1/2))^(2/3)+3*(27+3*57^(1/2))^(1/3)+6)/(27+3*5
7^(1/2))^(1/3)*x)-_C3*exp(-1/6/(27+3*57^(1/2))^(1/3)*((27+3*57^(1/2))^(2/3)-6*(2
7+3*57^(1/2))^(1/3)+6)*x)*sin(1/6/(27+3*57^(1/2))^(1/3)*3^(1/2)*((27+3*57^(1/2))
^(2/3)-6)*x)+_C4*exp(-1/6/(27+3*57^(1/2))^(1/3)*((27+3*57^(1/2))^(2/3)-6*(27+3*5
7^(1/2))^(1/3)+6)*x)*cos(1/6/(27+3*57^(1/2))^(1/3)*3^(1/2)*((27+3*57^(1/2))^(2/3
)-6)*x)