Internal problem ID [2105]
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: 33.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-7 y^{\prime \prime }-y^{\prime }+6 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$4)+diff(y(x),x$3)-7*diff(y(x),x$2)-diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} {\mathrm e}^{5 x}+c_{4} {\mathrm e}^{4 x}+c_{3} {\mathrm e}^{2 x}+c_{2} \right ) {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 36
DSolve[y''''[x]+y'''[x]-7*y''[x]-y'[x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-3 x}+c_2 e^{-x}+c_3 e^x+c_4 e^{2 x} \]