6.5.42 problem 41

Internal problem ID [1666]
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 : 41
Date solved : Tuesday, September 30, 2025 at 04:48:28 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {-6 x +y-3}{2 x -y-1} \end{align*}

✓ Maple. Time used: 0.235 (sec). Leaf size: 54

ode:=diff(y(x),x) = (-6*x+y(x)-3)/(2*x-y(x)-1); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {3 \operatorname {RootOf}\left (-1+\textit {\_Z}^{5}+\left (5 c_1 x +5 c_1 \right ) \textit {\_Z}^{4}\right )^{4} c_1 x -1}{\operatorname {RootOf}\left (-1+\textit {\_Z}^{5}+\left (5 c_1 x +5 c_1 \right ) \textit {\_Z}^{4}\right )^{4} c_1} \]

✓ Mathematica. Time used: 60.059 (sec). Leaf size: 3011

ode=D[y[x],x]==(-6*x+y[x]-3)/(2*x-y[x]-1); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✓ Sympy. Time used: 0.705 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + (6*x - y(x) + 3)/(2*x - y(x) - 1),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \log {\left (x + 1 \right )} = C_{1} - \log {\left (\sqrt [5]{-3 + \frac {y{\left (x \right )} + 3}{x + 1}} \left (2 + \frac {y{\left (x \right )} + 3}{x + 1}\right )^{\frac {4}{5}} \right )} \]