30.5.31 problem 31

Internal problem ID [7530]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.6, Substitutions and Transformations. Exercises. page 76
Problem number : 31
Date solved : Tuesday, September 30, 2025 at 04:42:41 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.036 (sec). Leaf size: 198

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

\[ y = \frac {\frac {\left (1-i \sqrt {3}\right ) \left (24 \left (x -\frac {1}{2}\right ) \sqrt {3}\, c_1^{2} \sqrt {\frac {108 \left (x -\frac {1}{2}\right )^{2} c_1 -8 x +4}{c_1}}+8+432 \left (x -\frac {1}{2}\right )^{2} c_1^{2}+\left (-144 x +72\right ) c_1 \right )^{{2}/{3}}}{24}-\left (\frac {1}{6}+\left (-\frac {3}{2}+x \right ) c_1 \right ) \left (24 \left (x -\frac {1}{2}\right ) \sqrt {3}\, c_1^{2} \sqrt {\frac {108 \left (x -\frac {1}{2}\right )^{2} c_1 -8 x +4}{c_1}}+8+432 \left (x -\frac {1}{2}\right )^{2} c_1^{2}+\left (-144 x +72\right ) c_1 \right )^{{1}/{3}}+2 \left (-i \sqrt {3}-1\right ) \left (-\frac {1}{12}+\left (x -\frac {1}{2}\right ) c_1 \right )}{\left (24 \left (x -\frac {1}{2}\right ) \sqrt {3}\, c_1^{2} \sqrt {\frac {108 \left (x -\frac {1}{2}\right )^{2} c_1 -8 x +4}{c_1}}+8+432 \left (x -\frac {1}{2}\right )^{2} c_1^{2}+\left (-144 x +72\right ) c_1 \right )^{{1}/{3}} c_1} \]

✓ Mathematica. Time used: 60.058 (sec). Leaf size: 2563

ode=(2*x-y[x])+(4*x+y[x]-3)*D[y[x],x]==0; 
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(2*x + (4*x + y(x) - 3)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out