67.1.22 problem 2.3 (L)

Internal problem ID [16287]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.3 (L)
Date solved : Thursday, October 02, 2025 at 10:45:22 AM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} y^{\prime \prime \prime \prime }&=1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=diff(diff(diff(diff(y(x),x),x),x),x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{24} x^{4}+\frac {1}{6} c_1 \,x^{3}+\frac {1}{2} c_2 \,x^{2}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 31

ode=D[y[x],{x,4}]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^4}{24}+c_4 x^3+c_3 x^2+c_2 x+c_1 \end{align*}

✓ Sympy. Time used: 0.037 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 4)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} x^{3} + \frac {x^{4}}{24} \]