23.5.101 problem 101

Internal problem ID [6710]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 101
Date solved : Tuesday, September 30, 2025 at 03:51:02 PM
CAS classification : [[_3rd_order, _exact, _linear, _homogeneous]]

\begin{align*} y-x y^{\prime }+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

ode:=y(x)-x*diff(y(x),x)+2*x^2*diff(diff(y(x),x),x)+x^3*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

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

ode=y[x] - x*D[y[x],x] + 2*x^2*D[y[x],{x,2}] + x^3*D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1}{x}+c_2 x+c_3 x \log (x) \end{align*}

✓ Sympy. Time used: 0.147 (sec). Leaf size: 15

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

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