56.28.1 problem Ex 1

Internal problem ID [14229]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 51. Cauchy linear equation. Page 114
Problem number : Ex 1
Date solved : Thursday, October 02, 2025 at 09:26:56 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} -y+x y^{\prime }+x^{3} y^{\prime \prime \prime }&=x \ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

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

\[ y = x \left (\frac {\ln \left (x \right )^{4}}{24}+c_1 +c_2 \ln \left (x \right )+c_3 \ln \left (x \right )^{2}\right ) \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to \frac {1}{24} x \log ^4(x)+c_1 x+c_3 x \log ^2(x)+c_2 x \log (x) \end{align*}

✓ Sympy. Time used: 0.203 (sec). Leaf size: 24

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

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