ODE
\[ y'''(x)-y''(x)+y'(x)+y(x)=0 \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00804701 (sec), leaf count = 81
\[\left \{\left \{y(x)\to c_1 e^{x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2+\text {$\#$1}+1\& ,1\right ]}+c_2 e^{x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2+\text {$\#$1}+1\& ,2\right ]}+c_3 e^{x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2+\text {$\#$1}+1\& ,3\right ]}\right \}\right \}\]
Maple ✓
cpu = 0.032 (sec), leaf count = 170
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac { \left ( \left ( 17+3\,\sqrt {33} \right ) ^{{\frac {2}{3}}}-\sqrt [3]{17+3\,\sqrt {33}}-2 \right ) x}{3\,\sqrt [3]{17+3\,\sqrt {33}}}}}}+{\it \_C2}\,{{\rm e}^{{\frac { \left ( \left ( 17+3\,\sqrt {33} \right ) ^{{\frac {2}{3}}}+2\,\sqrt [3]{17+3\,\sqrt {33}}-2 \right ) x}{6\,\sqrt [3]{17+3\,\sqrt {33}}}}}}\sin \left ( {\frac {\sqrt {3} \left ( \left ( 17+3\,\sqrt {33} \right ) ^{{\frac {2}{3}}}+2 \right ) x}{6\,\sqrt [3]{17+3\,\sqrt {33}}}} \right ) +{\it \_C3}\,{{\rm e}^{{\frac { \left ( \left ( 17+3\,\sqrt {33} \right ) ^{{\frac {2}{3}}}+2\,\sqrt [3]{17+3\,\sqrt {33}}-2 \right ) x}{6\,\sqrt [3]{17+3\,\sqrt {33}}}}}}\cos \left ( {\frac {\sqrt {3} \left ( \left ( 17+3\,\sqrt {33} \right ) ^{{\frac {2}{3}}}+2 \right ) x}{6\,\sqrt [3]{17+3\,\sqrt {33}}}} \right ) \right \} \] 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),'implicit')
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)*((17+3*33^(1/2))^(2/3)+2*(17+3*33^(1/2))^(1/3)-2)*x)*sin(1/6/(17+3*33^(1/2))^(1/3)*3^(1/2)*((17+3*33^(1/2))^(2/3)+2)*x)+_C3*exp(1/6/(17+3*33^(1/2))^(1/3)*((17+3*33^(1/2))^(2/3)+2*(17+3*33^(1/2))^(1/3)-2)*x)*cos(1/6/(17+3*33^(1/2))^(1/3)*3^(1/2)*((17+3*33^(1/2))^(2/3)+2)*x)