82.8.16 problem 36-17

Internal problem ID [21887]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 36. Nonlinear differential equations. Page 1203
Problem number : 36-17
Date solved : Thursday, October 02, 2025 at 08:05:45 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

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

\begin{align*} y &= \frac {x^{2}}{2}+c_1 \\ y &= -x +1+{\mathrm e}^{-x} c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 32

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

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

✗ Sympy

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

NotImplementedError : The given ODE -sqrt((4*x**2 + y(x))*y(x))/2 + y(x)/2 + Derivative(y(x), x) cannot be solved by the factorable group method