28.1.104 problem 127

Internal problem ID [4410]
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 : 127
Date solved : Tuesday, March 04, 2025 at 06:40:15 PM
CAS classification : [[_homogeneous, `class C`], _rational]

\begin{align*} y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 26

ode:=diff(y(x),x) = 2*(y(x)+2)^2/(x+y(x)-1)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = -2+\tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\tan \left (\textit {\_Z} \right )\right )+\ln \left (x -3\right )+c_{1} \right )\right ) \left (-x +3\right ) \]

✓ Mathematica. Time used: 0.168 (sec). Leaf size: 27

ode=D[y[x],x]==2*( (y[x]+2)/(x+y[x]-1) )^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [2 \arctan \left (\frac {3-x}{y(x)+2}\right )+\log (y(x)+2)=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*(y(x) + 2)**2/(x + y(x) - 1)**2 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out