75.14.1 problem 327

Internal problem ID [16836]
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 : Thursday, March 13, 2025 at 08:52:55 AM
CAS classification : [[_high_order, _quadrature]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 35

ode:=diff(diff(diff(diff(y(x),x),x),x),x) = x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{5}}{120}+\frac {c_{1} x^{3}}{6}+\frac {c_{2} x^{2}}{2}+\frac {\left (3 c_{1}^{2}+2 c_{3} \right ) x}{2}+c_4 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 31

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

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

✓ Sympy. Time used: 0.088 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} x^{3} + \frac {x^{5}}{120} \]