64.1.6 problem 2(b)

Internal problem ID [13180]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number : 2(b)
Date solved : Monday, March 31, 2025 at 07:36:19 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }+y&=x^{3} y^{3} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

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

\begin{align*} y &= \frac {1}{\sqrt {-2 x +c_1}\, x} \\ y &= -\frac {1}{\sqrt {-2 x +c_1}\, x} \\ \end{align*}

✓ Mathematica. Time used: 0.472 (sec). Leaf size: 44

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

\begin{align*} y(x)\to -\frac {1}{\sqrt {x^2 (-2 x+c_1)}} \\ y(x)\to \frac {1}{\sqrt {x^2 (-2 x+c_1)}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.632 (sec). Leaf size: 29

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

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