6.5.26 problem 23

Internal problem ID [1650]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 23
Date solved : Tuesday, September 30, 2025 at 04:41:30 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 14

ode:=diff(y(x),x) = (x^3+y(x)^3)/x/y(x)^2; 
ic:=[y(1) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \left (3 \ln \left (x \right )+27\right )^{{1}/{3}} x \]

✓ Mathematica. Time used: 0.114 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to \sqrt [3]{3} x \sqrt [3]{\log (x)+9} \end{align*}

✓ Sympy. Time used: 0.981 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \sqrt [3]{x^{3} \left (3 \log {\left (x \right )} + 27\right )} \]