23.1.148 problem 149

Internal problem ID [4755]
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 : 149
Date solved : Tuesday, September 30, 2025 at 08:30:35 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=1+x^{3}+y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=x*diff(y(x),x) = 1+x^3+y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{2} x^{3}-1+c_1 x \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 18

ode=x*D[y[x],x]==1+x^3+y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^3}{2}+c_1 x-1 \end{align*}

✓ Sympy. Time used: 0.156 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3 + x*Derivative(y(x), x) - y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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