82.8.19 problem 36-20

Internal problem ID [21890]
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 : 36-20
Date solved : Thursday, October 02, 2025 at 08:05:46 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 35

ode:=y(x)*diff(y(x),x)^2-(x*y(x)+y(x)^2+x)*diff(y(x),x)+x^2+x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✗ Mathematica

ode=x*D[y[x],x]^2-(x*y[x]+y[x]^2+x)*D[y[x],x]+x^2+x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

Timed Out