ODE
\[ -3 y'''(x)+y''''(x)+y''(x)-y'(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0394146 (sec), leaf count = 143
\[\left \{\left \{y(x)\to \frac {c_1 e^{x \text {Root}\left [\text {$\#$1}^3-3 \text {$\#$1}^2+\text {$\#$1}-1\& ,1\right ]}}{\text {Root}\left [\text {$\#$1}^3-3 \text {$\#$1}^2+\text {$\#$1}-1\& ,1\right ]}+\frac {c_3 e^{x \text {Root}\left [\text {$\#$1}^3-3 \text {$\#$1}^2+\text {$\#$1}-1\& ,3\right ]}}{\text {Root}\left [\text {$\#$1}^3-3 \text {$\#$1}^2+\text {$\#$1}-1\& ,3\right ]}+\frac {c_2 e^{x \text {Root}\left [\text {$\#$1}^3-3 \text {$\#$1}^2+\text {$\#$1}-1\& ,2\right ]}}{\text {Root}\left [\text {$\#$1}^3-3 \text {$\#$1}^2+\text {$\#$1}-1\& ,2\right ]}+c_4\right \}\right \}\]
Maple ✓
cpu = 0.035 (sec), leaf count = 172
\[ \left \{ y \left ( x \right ) ={\it \_C1}+{\it \_C2}\,{{\rm e}^{{\frac { \left ( \left ( 27+3\,\sqrt {57} \right ) ^{{\frac {2}{3}}}+3\,\sqrt [3]{27+3\,\sqrt {57}}+6 \right ) x}{3\,\sqrt [3]{27+3\,\sqrt {57}}}}}}-{\it \_C3}\,{{\rm e}^{-{\frac { \left ( \left ( 27+3\,\sqrt {57} \right ) ^{{\frac {2}{3}}}-6\,\sqrt [3]{27+3\,\sqrt {57}}+6 \right ) x}{6\,\sqrt [3]{27+3\,\sqrt {57}}}}}}\sin \left ( {\frac {\sqrt {3} \left ( \left ( 27+3\,\sqrt {57} \right ) ^{{\frac {2}{3}}}-6 \right ) x}{6\,\sqrt [3]{27+3\,\sqrt {57}}}} \right ) +{\it \_C4}\,{{\rm e}^{-{\frac { \left ( \left ( 27+3\,\sqrt {57} \right ) ^{{\frac {2}{3}}}-6\,\sqrt [3]{27+3\,\sqrt {57}}+6 \right ) x}{6\,\sqrt [3]{27+3\,\sqrt {57}}}}}}\cos \left ( {\frac {\sqrt {3} \left ( \left ( 27+3\,\sqrt {57} \right ) ^{{\frac {2}{3}}}-6 \right ) x}{6\,\sqrt [3]{27+3\,\sqrt {57}}}} \right ) \right \} \] 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),'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*57^(1/2))^(1/3)*x)-_C3*exp(-1/6/(27+3*57^(1/2))^(1/3)*((27+3*57^(1/2))^(2/3)-6*(27+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*57^(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)