58.13.19 problem 19

Internal problem ID [14830]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 19
Date solved : Thursday, October 02, 2025 at 09:55:30 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{3} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 23

ode:=x^3*diff(diff(diff(y(x),x),x),x)-x^2*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-2*y(x) = x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x \left (4 c_3 \ln \left (x \right )+4 c_2 x +x^{2}+4 c_1 \right )}{4} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 29

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

\begin{align*} y(x)&\to \frac {1}{4} x \left (x^2+4 c_3 x+4 c_2 \log (x)+4 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.175 (sec). Leaf size: 19

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

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