75.14.1 problem 327

Internal problem ID [16915]
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 ODEs). Section 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 327
Date solved : Tuesday, January 28, 2025 at 09:40:50 AM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} y^{\prime \prime \prime \prime }&=x \end{align*}

✓ Solution by Maple

Time used: 0.002 (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: 0.003 (sec). Leaf size: 31

DSolve[D[y[x],{x,4}]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^5}{120}+c_4 x^3+c_3 x^2+c_2 x+c_1 \]