23.1.52 problem 46

Internal problem ID [4659]
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 : 46
Date solved : Tuesday, September 30, 2025 at 07:38:25 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=2 x -\left (x^{2}+1\right ) y+y^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 36

ode:=diff(y(x),x) = 2*x-(x^2+1)*y(x)+y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{2}+1+\frac {{\mathrm e}^{\frac {x \left (x^{2}+3\right )}{3}}}{c_1 -\int {\mathrm e}^{\frac {x \left (x^{2}+3\right )}{3}}d x} \]

✓ Mathematica. Time used: 0.268 (sec). Leaf size: 58

ode=D[y[x],x]==2*x-(1+x^2)*y[x]+y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{\frac {x^3}{3}+x}}{-\int _1^xe^{\frac {K[1]^3}{3}+K[1]}dK[1]+c_1}+x^2+1\\ y(x)&\to x^2+1 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x + (x**2 + 1)*y(x) - y(x)**2 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

TypeError : bad operand type for unary -: list