23.1.233 problem 229

Internal problem ID [4840]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 229
Date solved : Tuesday, September 30, 2025 at 08:43:56 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} \left (1+x \right ) y^{\prime }&=\left (1-x y^{3}\right ) y \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 178

ode:=(1+x)*diff(y(x),x) = (1-x*y(x)^3)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {2^{{2}/{3}} {\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_1 \right )^{2}\right )}^{{1}/{3}} \left (1+x \right )}{3 x^{4}+8 x^{3}+6 x^{2}+4 c_1} \\ y &= -\frac {{\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_1 \right )^{2}\right )}^{{1}/{3}} 2^{{2}/{3}} \left (1+i \sqrt {3}\right ) \left (1+x \right )}{6 x^{4}+16 x^{3}+12 x^{2}+8 c_1} \\ y &= \frac {{\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_1 \right )^{2}\right )}^{{1}/{3}} 2^{{2}/{3}} \left (i \sqrt {3}-1\right ) \left (1+x \right )}{6 x^{4}+16 x^{3}+12 x^{2}+8 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.192 (sec). Leaf size: 124

ode=(1+x)*D[y[x],x]==(1-x*y[x]^3)*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {(-2)^{2/3} (x+1)}{\sqrt [3]{-3 x^4-8 x^3-6 x^2-4 c_1}}\\ y(x)&\to -\frac {2^{2/3} (x+1)}{\sqrt [3]{-3 x^4-8 x^3-6 x^2-4 c_1}}\\ y(x)&\to \frac {\sqrt [3]{-1} 2^{2/3} (x+1)}{\sqrt [3]{-3 x^4-8 x^3-6 x^2-4 c_1}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 1.875 (sec). Leaf size: 133

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 1)*Derivative(y(x), x) - (-x*y(x)**3 + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = 2^{\frac {2}{3}} \left (x + 1\right ) \sqrt [3]{\frac {1}{C_{1} + 3 x^{4} + 8 x^{3} + 6 x^{2}}}, \ y{\left (x \right )} = \frac {2^{\frac {2}{3}} \left (- x + \sqrt {3} i x - 1 + \sqrt {3} i\right ) \sqrt [3]{\frac {1}{C_{1} + 3 x^{4} + 8 x^{3} + 6 x^{2}}}}{2}, \ y{\left (x \right )} = \frac {2^{\frac {2}{3}} \left (- x - \sqrt {3} i x - 1 - \sqrt {3} i\right ) \sqrt [3]{\frac {1}{C_{1} + 3 x^{4} + 8 x^{3} + 6 x^{2}}}}{2}\right ] \]