81.1.36 problem 2-34

Internal problem ID [21481]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 2. Separable differential equations
Problem number : 2-34
Date solved : Thursday, October 02, 2025 at 07:40:05 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.021 (sec). Leaf size: 44

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

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

✓ Mathematica. Time used: 60.065 (sec). Leaf size: 1461

ode=(x-y[x])+(x-4*y[x])*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: 85.651 (sec). Leaf size: 1035

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

\[ \text {Solution too large to show} \]