54.1.20 problem 20

Internal problem ID [11334]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 20
Date solved : Tuesday, September 30, 2025 at 07:43:16 PM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }-y^{2}+\left (x^{2}+1\right ) y-2 x&=0 \end{align*}

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

ode:=diff(y(x),x)-y(x)^2+(x^2+1)*y(x)-2*x = 0; 
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: 0.191 (sec). Leaf size: 58

ode=D[y[x],x] - y[x]^2 +(x^2 + 1)*y[x] - 2*x==0; 
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