28.1.57 problem 58

Internal problem ID [4363]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 58
Date solved : Sunday, March 30, 2025 at 03:10:28 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 16

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

\[ -y c_1 +x -\frac {y^{4}}{3} = 0 \]

✓ Mathematica. Time used: 0.108 (sec). Leaf size: 997

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 1.983 (sec). Leaf size: 1017

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

\[ \text {Solution too large to show} \]