ODE
\[ y''''(x)-2 y''(x)+y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.145278 (sec), leaf count = 35
\[\left \{\left \{y(x)\to e^{-x} \left (c_3 e^{2 x}+x \left (c_4 e^{2 x}+c_2\right )+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 27
\[[y \left (x \right ) = {\mathrm e}^{-x} \textit {\_C1} +\textit {\_C2} \,{\mathrm e}^{-x} x +\textit {\_C3} \,{\mathrm e}^{x}+\textit {\_C4} \,{\mathrm e}^{x} x]\] Mathematica raw input
DSolve[y[x] - 2*y''[x] + y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + E^(2*x)*C[3] + x*(C[2] + E^(2*x)*C[4]))/E^x}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)-2*diff(diff(y(x),x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = exp(-x)*_C1+_C2*exp(-x)*x+_C3*exp(x)+_C4*exp(x)*x]