23.5.99 problem 99

Internal problem ID [6708]
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 : 99
Date solved : Tuesday, September 30, 2025 at 03:51:01 PM
CAS classification : [[_3rd_order, _missing_y]]

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

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

ode:=x*diff(y(x),x)-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);
 

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 35

ode=x*D[y[x],x] - 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 {1}{4} (2 c_1-c_2) x^2+\frac {1}{2} c_2 x^2 \log (x)+c_3 \end{align*}

✓ Sympy. Time used: 0.093 (sec). Leaf size: 17

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

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