68.15.48 problem 51

Internal problem ID [17774]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 51
Date solved : Thursday, October 02, 2025 at 02:28:03 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} -y+x y^{\prime }+x^{3} y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=x^3*diff(diff(diff(y(x),x),x),x)+x*diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 22

ode=x^3*D[y[x],{x,3}]+x*D[y[x],x]-y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x \left (c_3 \log ^2(x)+c_2 \log (x)+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.104 (sec). Leaf size: 17

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

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