75.15.19 problem 450

Internal problem ID [16970]
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 15.2 Homogeneous differential equations with constant coefficients. Exercises page 121
Problem number : 450
Date solved : Tuesday, January 28, 2025 at 09:43:56 AM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} y^{\left (5\right )}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(diff(y(x),x$5)=0,y(x), singsol=all)
 

\[ y = \frac {1}{24} c_{1} x^{4}+\frac {1}{6} c_{2} x^{3}+\frac {1}{2} x^{2} c_{3} +c_4 x +c_5 \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 27

DSolve[D[y[x],{x,5}]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (x (x (c_5 x+c_4)+c_3)+c_2)+c_1 \]