28.1.44 problem 45

Internal problem ID [4350]
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 : 45
Date solved : Sunday, March 30, 2025 at 03:09:12 AM
CAS classification : [[_homogeneous, `class D`]]

\begin{align*} y-2 x^{3} \tan \left (\frac {y}{x}\right )-x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 15

ode:=y(x)-2*x^3*tan(y(x)/x)-x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arcsin \left ({\mathrm e}^{-x^{2}} c_1 \right ) x \]

✓ Mathematica. Time used: 56.981 (sec). Leaf size: 23

ode=y[x]-2*x^3*Tan[y[x]/x]-x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to x \arcsin \left (e^{-x^2+c_1}\right ) \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

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

Timed Out