81.15.6 problem 19-6

Internal problem ID [21714]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 19. Change of variables. Page 483
Problem number : 19-6
Date solved : Thursday, October 02, 2025 at 08:00:43 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x -2 y+1+\left (4 x -3 y-6\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.206 (sec). Leaf size: 56

ode:=x-2*y(x)+1+(4*x-3*y(x)-6)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-x +3\right ) {\operatorname {RootOf}\left (-4+\left (3 c_1 \,x^{4}-36 c_1 \,x^{3}+162 c_1 \,x^{2}-324 c_1 x +243 c_1 \right ) \textit {\_Z}^{20}-\textit {\_Z}^{4}\right )}^{4}}{3}-\frac {x}{3}+3 \]

✓ Mathematica. Time used: 60.042 (sec). Leaf size: 1511

ode=(x-2*y[x]+1)+(4*x-3*y[x]-6)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 0.739 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (4*x - 3*y(x) - 6)*Derivative(y(x), x) - 2*y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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