85.24.7 problem 7

Internal problem ID [22584]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 57
Problem number : 7
Date solved : Thursday, October 02, 2025 at 08:53:32 PM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.042 (sec). Leaf size: 21

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

\[ x -\frac {\ln \left (x^{2}+y^{2}\right )}{2}-y+c_1 = 0 \]

✓ Mathematica. Time used: 0.154 (sec). Leaf size: 28

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

\[ \text {Solve}\left [\frac {1}{2} e^{2 y(x)-2 x} \left (x^2+y(x)^2\right )=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out