ODE
\[ y''''(x)-12 y''(x)+27 y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00979765 (sec), leaf count = 47
\[\left \{\left \{y(x)\to c_1 e^{\sqrt {3} x}+c_2 e^{-\sqrt {3} x}+c_3 e^{-3 x}+c_4 e^{3 x}\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 34
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{3\,x}}+{\it \_C2}\,{{\rm e}^{-3\,x}}+{\it \_C3}\,{{\rm e}^{\sqrt {3}x}}+{\it \_C4}\,{{\rm e}^{-\sqrt {3}x}} \right \} \] Mathematica raw input
DSolve[27*y[x] - 12*y''[x] + y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^(Sqrt[3]*x)*C[1] + C[2]/E^(Sqrt[3]*x) + C[3]/E^(3*x) + E^(3*x)*C[4]}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)-12*diff(diff(y(x),x),x)+27*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*exp(3*x)+_C2*exp(-3*x)+_C3*exp(3^(1/2)*x)+_C4*exp(-3^(1/2)*x)