Internal problem ID [2113]
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: 41.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}+y^{\prime \prime \prime \prime }-13 y^{\prime \prime \prime }-13 y^{\prime \prime }+36 y^{\prime }+36 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$5)+diff(y(x),x$4)-13*diff(y(x),x$3)-13*diff(y(x),x$2)+36*diff(y(x),x)+36*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} {\mathrm e}^{6 x}+c_{2} {\mathrm e}^{5 x}+c_{5} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{x}+c_{4} \right ) {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 42
DSolve[y'''''[x]+y''''[x]-13*y'''[x]-13*y''[x]+36*y'[x]+36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (e^x \left (c_3 e^x+e^{4 x} \left (c_5 e^x+c_4\right )+c_2\right )+c_1\right ) \]