85.28.3 problem 3

Internal problem ID [22610]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 60
Problem number : 3
Date solved : Thursday, October 02, 2025 at 08:55:01 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

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

\[ y = \ln \left (x \right ) c_1 x +\frac {x^{2}}{2}+\left (-c_1 +c_2 \right ) x +c_3 \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 30

ode=x*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-c_1) x+c_1 x \log (x)+c_2 \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 19

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

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