28.1.84 problem 87

Internal problem ID [4390]
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 : 87
Date solved : Tuesday, March 04, 2025 at 06:35:57 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.087 (sec). Leaf size: 135

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

\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {2 x^{3} \sqrt {x^{2}+3 c_{1}}-2 x^{4}-6 x \sqrt {x^{2}+3 c_{1}}\, c_{1} +3 c_{1} x^{2}-9 c_{1}^{2}}{-27 x +27 \sqrt {x^{2}+3 c_{1}}} \\ y \left (x \right ) &= \frac {2 x^{3} \sqrt {x^{2}+3 c_{1}}+2 x^{4}-6 x \sqrt {x^{2}+3 c_{1}}\, c_{1} -3 c_{1} x^{2}+9 c_{1}^{2}}{27 x +27 \sqrt {x^{2}+3 c_{1}}} \\ \end{align*}

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out