ODE
\[ y'''(x)-y''(x)+y'(x)=0 \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.124316 (sec), leaf count = 75
\[\left \{\left \{y(x)\to \frac {e^{x/2} \left (\left (3 c_1+\sqrt {3} c_2\right ) \sin \left (\frac {\sqrt {3} x}{2}\right )+\left (\sqrt {3} c_1-3 c_2\right ) \cos \left (\frac {\sqrt {3} x}{2}\right )\right )}{2 \sqrt {3}}+c_3\right \}\right \}\]
Maple ✓
cpu = 0.006 (sec), leaf count = 32
\[ \left \{ y \left ( x \right ) ={\it \_C1}+{\it \_C2}\,\sin \left ( {\frac {\sqrt {3}x}{2}} \right ) {{\rm e}^{{\frac {x}{2}}}}+{\it \_C3}\,\cos \left ( {\frac {\sqrt {3}x}{2}} \right ) {{\rm e}^{{\frac {x}{2}}}} \right \} \] Mathematica raw input
DSolve[y'[x] - y''[x] + y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[3] + (E^(x/2)*((Sqrt[3]*C[1] - 3*C[2])*Cos[(Sqrt[3]*x)/2] + (3*C[1] + Sqrt[3]*C[2])*Sin[(Sqrt[3]*x)/2]))/(2*Sqrt[3])}}
Maple raw input
dsolve(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*sin(1/2*3^(1/2)*x)*exp(1/2*x)+_C3*cos(1/2*3^(1/2)*x)*exp(1/2*x)