ODE
\[ y'''(x)-y''(x)+y'(x)+y(x)=0 \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.155694 (sec), leaf count = 81
\[\left \{\left \{y(x)\to c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2+\text {$\#$1}+1\& ,1\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2+\text {$\#$1}+1\& ,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2+\text {$\#$1}+1\& ,3\right ]\right )\right \}\right \}\]
Maple ✓
cpu = 0.161 (sec), leaf count = 180
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{-\frac {\left (\left (17+3 \sqrt {33}\right )^{\frac {2}{3}}-\left (17+3 \sqrt {33}\right )^{\frac {1}{3}}-2\right ) x}{3 \left (17+3 \sqrt {33}\right )^{\frac {1}{3}}}}+\textit {\_C2} \,{\mathrm e}^{\frac {\left (-2+\left (17+3 \sqrt {33}\right )^{\frac {2}{3}}+2 \left (17+3 \sqrt {33}\right )^{\frac {1}{3}}\right ) x}{6 \left (17+3 \sqrt {33}\right )^{\frac {1}{3}}}} \sin \left (\frac {\left (\left (17+3 \sqrt {33}\right )^{\frac {2}{3}} \sqrt {3}+2 \sqrt {3}\right ) x}{6 \left (17+3 \sqrt {33}\right )^{\frac {1}{3}}}\right )+\textit {\_C3} \,{\mathrm e}^{\frac {\left (-2+\left (17+3 \sqrt {33}\right )^{\frac {2}{3}}+2 \left (17+3 \sqrt {33}\right )^{\frac {1}{3}}\right ) x}{6 \left (17+3 \sqrt {33}\right )^{\frac {1}{3}}}} \cos \left (\frac {\left (\left (17+3 \sqrt {33}\right )^{\frac {2}{3}} \sqrt {3}+2 \sqrt {3}\right ) x}{6 \left (17+3 \sqrt {33}\right )^{\frac {1}{3}}}\right )\right ]\] Mathematica raw input
DSolve[y[x] + y'[x] - y''[x] + y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^(x*Root[1 + #1 - #1^2 + #1^3 & , 1, 0])*C[1] + E^(x*Root[1 + #1 - #1^2 + #1^3 & , 2, 0])*C[2] + E^(x*Root[1 + #1 - #1^2 + #1^3 & , 3, 0])*C[3]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)+diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(-1/3*((17+3*33^(1/2))^(2/3)-(17+3*33^(1/2))^(1/3)-2)/(17+3*33^(1/2))^(1/3)*x)+_C2*exp(1/6/(17+3*33^(1/2))^(1/3)*(-2+(17+3*33^(1/2))^(2/3)+2*(17+3*33^(1/2))^(1/3))*x)*sin(1/6/(17+3*33^(1/2))^(1/3)*((17+3*33^(1/2))^(2/3)*3^(1/2)+2*3^(1/2))*x)+_C3*exp(1/6/(17+3*33^(1/2))^(1/3)*(-2+(17+3*33^(1/2))^(2/3)+2*(17+3*33^(1/2))^(1/3))*x)*cos(1/6/(17+3*33^(1/2))^(1/3)*((17+3*33^(1/2))^(2/3)*3^(1/2)+2*3^(1/2))*x)]