ODE
\[ y''''(x)+5 y''(x)+6 y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00952887 (sec), leaf count = 50
\[\left \{\left \{y(x)\to c_4 \sin \left (\sqrt {2} x\right )+c_2 \sin \left (\sqrt {3} x\right )+c_3 \cos \left (\sqrt {2} x\right )+c_1 \cos \left (\sqrt {3} x\right )\right \}\right \}\]
Maple ✓
cpu = 0.005 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( \sqrt {3}x \right ) +{\it \_C2}\,\cos \left ( \sqrt {3}x \right ) +{\it \_C3}\,\sin \left ( \sqrt {2}x \right ) +{\it \_C4}\,\cos \left ( \sqrt {2}x \right ) \right \} \] Mathematica raw input
DSolve[6*y[x] + 5*y''[x] + y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[3]*Cos[Sqrt[2]*x] + C[1]*Cos[Sqrt[3]*x] + C[4]*Sin[Sqrt[2]*x] + C[2]*Sin[Sqrt[3]*x]}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+5*diff(diff(y(x),x),x)+6*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*sin(3^(1/2)*x)+_C2*cos(3^(1/2)*x)+_C3*sin(2^(1/2)*x)+_C4*cos(2^(1/2)*x)