34.3.33 problem 26 (g)

Internal problem ID [7924]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 26 (g)
Date solved : Tuesday, September 30, 2025 at 05:10:07 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to \frac {x}{-\log (x)+c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.120 (sec). Leaf size: 8

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

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