Internal problem ID [2139]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 18, page 82
Problem number: 23.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}-y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }-6 y^{\prime \prime }+8 y^{\prime }-8 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x$5)-diff(y(x),x$4)+6*diff(y(x),x$3)-6*diff(y(x),x$2)+8*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{x}+c_{2} \sin \left (2 x \right )+c_{3} \cos \left (2 x \right )+c_{4} \sin \left (\sqrt {2}\, x \right )+c_{5} \cos \left (\sqrt {2}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 48
DSolve[y'''''[x]-y''''[x]+6*y'''[x]-6*y''[x]+8*y'[x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_5 e^x+c_1 \cos (2 x)+c_3 \cos \left (\sqrt {2} x\right )+c_2 \sin (2 x)+c_4 \sin \left (\sqrt {2} x\right ) \]