28.1.86 problem 89

Internal problem ID [4392]
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 : 89
Date solved : Sunday, March 30, 2025 at 03:14:13 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.216 (sec). Leaf size: 123

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

\begin{align*} y &= -x^{2} \operatorname {RootOf}\left (4 c_1 \,x^{2} \textit {\_Z}^{4}+8 c_1 x \,\textit {\_Z}^{2}+4 c_1 -\textit {\_Z} \right )^{3}+x \operatorname {RootOf}\left (4 c_1 \,x^{2} \textit {\_Z}^{4}+8 c_1 x \,\textit {\_Z}^{2}+4 c_1 -\textit {\_Z} \right ) \\ y &= -x^{2} \operatorname {RootOf}\left (4 c_1 \,x^{2} \textit {\_Z}^{4}-16 c_1 x \,\textit {\_Z}^{2}+16 c_1 -\textit {\_Z} \right )^{3}+x \operatorname {RootOf}\left (4 c_1 \,x^{2} \textit {\_Z}^{4}-16 c_1 x \,\textit {\_Z}^{2}+16 c_1 -\textit {\_Z} \right ) \\ \end{align*}

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out