30.6.21 problem 22

Internal problem ID [7556]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Review problems. page 79
Problem number : 22
Date solved : Tuesday, September 30, 2025 at 04:48:58 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x -2 y-8+\left (x -3 y-6\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.183 (sec). Leaf size: 62

ode:=2*x-2*y(x)-8+(x-3*y(x)-6)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-1+c_1 \left (2 x -9\right ) \operatorname {RootOf}\left (-1+3 \textit {\_Z}^{5}+\left (5 c_1 x -15 c_1 \right ) \textit {\_Z}^{4}\right )^{4}}{3 \operatorname {RootOf}\left (-1+3 \textit {\_Z}^{5}+\left (5 c_1 x -15 c_1 \right ) \textit {\_Z}^{4}\right )^{4} c_1} \]

✓ Mathematica. Time used: 60.077 (sec). Leaf size: 3061

ode=(2*x-2*y[x]-8)+(x-3*y[x]-6)*D[y[x],x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✓ Sympy. Time used: 0.799 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (x - 3*y(x) - 6)*Derivative(y(x), x) - 2*y(x) - 8,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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