##### 4.45.42 $$-3 y'''(x)+y''''(x)+y''(x)-y'(x)=0$$

ODE
$-3 y'''(x)+y''''(x)+y''(x)-y'(x)=0$ ODE Classiﬁcation

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica
cpu = 0.174669 (sec), leaf count = 143

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

Maple
cpu = 0.176 (sec), leaf count = 182

$\left [y \left (x \right ) = \textit {\_C1} +\textit {\_C2} \,{\mathrm e}^{\frac {\left (\left (27+3 \sqrt {57}\right )^{\frac {2}{3}}+3 \left (27+3 \sqrt {57}\right )^{\frac {1}{3}}+6\right ) x}{3 \left (27+3 \sqrt {57}\right )^{\frac {1}{3}}}}-\textit {\_C3} \,{\mathrm e}^{-\frac {\left (6+\left (27+3 \sqrt {57}\right )^{\frac {2}{3}}-6 \left (27+3 \sqrt {57}\right )^{\frac {1}{3}}\right ) x}{6 \left (27+3 \sqrt {57}\right )^{\frac {1}{3}}}} \sin \left (\frac {\left (\left (27+3 \sqrt {57}\right )^{\frac {2}{3}} \sqrt {3}-6 \sqrt {3}\right ) x}{6 \left (27+3 \sqrt {57}\right )^{\frac {1}{3}}}\right )+\textit {\_C4} \,{\mathrm e}^{-\frac {\left (6+\left (27+3 \sqrt {57}\right )^{\frac {2}{3}}-6 \left (27+3 \sqrt {57}\right )^{\frac {1}{3}}\right ) x}{6 \left (27+3 \sqrt {57}\right )^{\frac {1}{3}}}} \cos \left (\frac {\left (\left (27+3 \sqrt {57}\right )^{\frac {2}{3}} \sqrt {3}-6 \sqrt {3}\right ) x}{6 \left (27+3 \sqrt {57}\right )^{\frac {1}{3}}}\right )\right ]$ 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))

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*
57^(1/2))^(1/3)*x)-_C3*exp(-1/6/(27+3*57^(1/2))^(1/3)*(6+(27+3*57^(1/2))^(2/3)-6
*(27+3*57^(1/2))^(1/3))*x)*sin(1/6/(27+3*57^(1/2))^(1/3)*((27+3*57^(1/2))^(2/3)*
3^(1/2)-6*3^(1/2))*x)+_C4*exp(-1/6/(27+3*57^(1/2))^(1/3)*(6+(27+3*57^(1/2))^(2/3
)-6*(27+3*57^(1/2))^(1/3))*x)*cos(1/6/(27+3*57^(1/2))^(1/3)*((27+3*57^(1/2))^(2/
3)*3^(1/2)-6*3^(1/2))*x)]