ODE
\[ y''''(x)-2 y''(x)+y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00803325 (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 = 0.007 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) = \left ( x{\it \_C2}+{\it \_C1} \right ) {{\rm e}^{-x}}+{{\rm e}^{x}} \left ( {\it \_C4}\,x+{\it \_C3} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = (_C2*x+_C1)*exp(-x)+exp(x)*(_C4*x+_C3)