ODE
\[ y''''(x)+y''(x)+y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00933399 (sec), leaf count = 56
\[\left \{\left \{y(x)\to e^{-x/2} \left (\left (c_3 e^x+c_1\right ) \sin \left (\frac {\sqrt {3} x}{2}\right )+\left (c_2 e^x+c_4\right ) \cos \left (\frac {\sqrt {3} x}{2}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.005 (sec), leaf count = 47
\[ \left \{ y \left ( x \right ) = \left ( {\it \_C2}\,{{\rm e}^{{\frac {x}{2}}}}+{\it \_C4}\,{{\rm e}^{-{\frac {x}{2}}}} \right ) \cos \left ( {\frac {\sqrt {3}x}{2}} \right ) +\sin \left ( {\frac {\sqrt {3}x}{2}} \right ) \left ( {\it \_C1}\,{{\rm e}^{{\frac {x}{2}}}}+{\it \_C3}\,{{\rm e}^{-{\frac {x}{2}}}} \right ) \right \} \] Mathematica raw input
DSolve[y[x] + y''[x] + y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((E^x*C[2] + C[4])*Cos[(Sqrt[3]*x)/2] + (C[1] + E^x*C[3])*Sin[(Sqrt[3]*x)/2])/E^(x/2)}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+diff(diff(y(x),x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C2*exp(1/2*x)+_C4*exp(-1/2*x))*cos(1/2*3^(1/2)*x)+sin(1/2*3^(1/2)*x)*(_C1*exp(1/2*x)+_C3*exp(-1/2*x))