23.1.362 problem 347

Internal problem ID [4969]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 347
Date solved : Tuesday, September 30, 2025 at 09:06:31 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

\[ y = -\frac {1}{x^{2}}+1+c_1 x \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to -\frac {1}{x^2}+c_1 x+1 \end{align*}

✓ Sympy. Time used: 0.162 (sec). Leaf size: 12

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

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