Internal problem ID [2238]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 24, page 109
Problem number: 5.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\left (5\right )}+y^{\prime \prime \prime \prime }=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(diff(y(x),x$5)+diff(y(x),x$4)=x^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{6}}{360}+\frac {x^{4}}{12}-\frac {x^{5}}{60}+\frac {c_{2} x^{3}}{6}+\frac {c_{3} x^{2}}{2}+{\mathrm e}^{-x} c_{1} +c_{4} x +c_{5} \]
✓ Solution by Mathematica
Time used: 0.134 (sec). Leaf size: 53
DSolve[y'''''[x]+y''''[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^6}{360}-\frac {x^5}{60}+\frac {x^4}{12}+c_5 x^3+c_4 x^2+c_3 x+c_1 e^{-x}+c_2 \]