87.7.7 problem 10

Internal problem ID [23348]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 57
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:39:24 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

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

\[ y = \frac {x^{2}}{2}+{\mathrm e}^{-x} c_1 +c_2 x +c_3 \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 27

ode=D[y[x],{x,3}]+D[y[x],{x,2}]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^2}{2}+c_3 x+c_1 e^{-x}+c_2 \end{align*}

✓ Sympy. Time used: 0.045 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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