22.1.87 problem 90

Internal problem ID [4393]
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 : 90
Date solved : Tuesday, September 30, 2025 at 07:27:29 AM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Maple. Time used: 0.066 (sec). Leaf size: 577

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

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

✓ Mathematica. Time used: 155.559 (sec). Leaf size: 51472

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

Too large to display

✗ Sympy

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

Timed Out