88.8.2 problem 2

Internal problem ID [24010]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 44
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:54:01 PM
CAS classification : [_rational, _Bernoulli]

\begin{align*} y^{3}+2 x y^{3}+1+3 x y^{2} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 92

ode:=y(x)^3+2*x*y(x)^3+1+3*x*y(x)^2*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 6.717 (sec). Leaf size: 99

ode=( y[x]^3+2*x*y[x]^3+1 )+( 3*x*y[x]^2 )*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.548 (sec). Leaf size: 85

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x)**3 + 3*x*y(x)**2*Derivative(y(x), x) + y(x)**3 + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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