Internal problem ID [2116]
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: 44.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}+3 y^{\prime \prime \prime }+2 y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$5)+3*diff(y(x),x$3)+2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +c_{2} \sin \left (\sqrt {2}\, x \right )+c_{3} \cos \left (\sqrt {2}\, x \right )+c_{4} \sin \left (x \right )+c_{5} \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.083 (sec). Leaf size: 52
DSolve[y'''''[x]+3*y'''[x]+2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -c_4 \cos (x)-\frac {c_2 \cos \left (\sqrt {2} x\right )}{\sqrt {2}}+c_3 \sin (x)+\frac {c_1 \sin \left (\sqrt {2} x\right )}{\sqrt {2}}+c_5 \]