Internal problem ID [15185]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 14. Differential equations admitting of
depression of their order. Exercises page 107
Problem number: 327.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _quadrature]]
\[ \boxed {y^{\prime \prime \prime \prime }=x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x$4)=x,y(x), singsol=all)
\[ y = \frac {x^{5}}{120}+\frac {c_{1} x^{3}}{6}+\frac {c_{2} x^{2}}{2}+\frac {\left (3 c_{1}^{2}+2 c_{3} \right ) x}{2}+c_{4} \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 31
DSolve[y''''[x]==x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^5}{120}+c_4 x^3+c_3 x^2+c_2 x+c_1 \]