ODE
\[ y'''(x)-y''(x)+y'(x)=0 \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.402583 (sec), leaf count = 75
\[\left \{\left \{y(x)\to \frac {1}{2} \left (c_1-\sqrt {3} c_2\right ) e^{x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+\frac {1}{2} \left (\sqrt {3} c_1+c_2\right ) e^{x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+c_3\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 32
\[\left [y \left (x \right ) = \textit {\_C1} +\textit {\_C2} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) {\mathrm e}^{\frac {x}{2}}+\textit {\_C3} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) {\mathrm e}^{\frac {x}{2}}\right ]\] Mathematica raw input
DSolve[y'[x] - y''[x] + y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[3] + (E^(x/2)*(C[1] - Sqrt[3]*C[2])*Cos[(Sqrt[3]*x)/2])/2 + (E^(x/2)*(Sqrt[3]*C[1] + C[2])*Sin[(Sqrt[3]*x)/2])/2}}
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))
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)]