Internal problem ID [2100]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 17, page 78
Problem number: 28.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-6 y^{\prime \prime }+8 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$4)-6*diff(y(x),x$2)+8*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{2 x}+{\mathrm e}^{-2 x} c_{2} +c_{3} {\mathrm e}^{\sqrt {2}\, x}+c_{4} {\mathrm e}^{-\sqrt {2}\, x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 47
DSolve[y''''[x]-6*y''[x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{\sqrt {2} x}+c_2 e^{-\sqrt {2} x}+c_3 e^{-2 x}+c_4 e^{2 x} \]