12.5.43 problem 42

Internal problem ID [1667]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 42
Date solved : Tuesday, March 04, 2025 at 01:27:16 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {2 x +y+1}{x +2 y-4} \end{align*}

✓ Maple. Time used: 3.465 (sec). Leaf size: 138

ode:=diff(y(x),x) = (2*x+y(x)+1)/(x+2*y(x)-4); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (5+x \right ) \operatorname {RootOf}\left (\textit {\_Z}^{16}+\left (2 c_1 \,x^{4}+16 c_1 \,x^{3}+48 c_1 \,x^{2}+64 c_1 x +32 c_1 \right ) \textit {\_Z}^{4}-c_1 \,x^{4}-8 c_1 \,x^{3}-24 c_1 \,x^{2}-32 c_1 x -16 c_1 \right )^{4}-2-x}{\operatorname {RootOf}\left (\textit {\_Z}^{16}+\left (2 c_1 \,x^{4}+16 c_1 \,x^{3}+48 c_1 \,x^{2}+64 c_1 x +32 c_1 \right ) \textit {\_Z}^{4}-c_1 \,x^{4}-8 c_1 \,x^{3}-24 c_1 \,x^{2}-32 c_1 x -16 c_1 \right )^{4}} \]

✓ Mathematica. Time used: 60.3 (sec). Leaf size: 8077

ode=D[y[x],x]==(2*x+y[x]+1)/(x+2*y[x]-4); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (2*x + y(x) + 1)/(x + 2*y(x) - 4),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out