23.3.478 problem 484

Internal problem ID [6192]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 484
Date solved : Tuesday, September 30, 2025 at 02:36:06 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} x^{3} y^{\prime \prime }&=b x +a \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

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

\[ y = \frac {a}{2 x}-b \ln \left (x \right )+c_1 x +c_2 \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \frac {a}{2 x}-b \log (x)+c_2 x+c_1 \end{align*}

✓ Sympy. Time used: 0.118 (sec). Leaf size: 17

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

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