78.8.33 problem 33

Internal problem ID [18152]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 33
Date solved : Thursday, March 13, 2025 at 11:45:19 AM
CAS classification : [_linear]

\begin{align*} \frac {y-x}{\left (x +y\right )^{3}}-\frac {2 x y^{\prime }}{\left (x +y\right )^{3}}&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=(y(x)-x)/(x+y(x))^3-2*x/(x+y(x))^3*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -x +\sqrt {x}\, c_{1} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 17

ode=(y[x]-x)/(x+y[x])^3 -  2*x/(x+y[x])^3  * D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -x+c_1 \sqrt {x} \]

✓ Sympy. Time used: 0.231 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*Derivative(y(x), x)/(x + y(x))**3 + (-x + y(x))/(x + y(x))**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sqrt {x} - x \]