83.2.2 problem 2

Internal problem ID [18977]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (A) at page 8
Problem number : 2
Date solved : Monday, March 31, 2025 at 06:27:56 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} y \left (1+x y\right )-x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

ode:=y(x)*(1+x*y(x))-x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {2 x}{x^{2}-2 c_1} \]

✓ Mathematica. Time used: 0.145 (sec). Leaf size: 23

ode=y[x]*(1+x*y[x])-x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {2 x}{x^2-2 c_1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.202 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*Derivative(y(x), x) + (x*y(x) + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {2 x}{C_{1} - x^{2}} \]