29.16.8 problem 451

Internal problem ID [5049]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 451
Date solved : Sunday, March 30, 2025 at 06:32:09 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.313 (sec). Leaf size: 45

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

\[ y = \frac {1}{2}-\frac {\left (-1+2 x \right ) \left (1+\operatorname {RootOf}\left (-3+\left (8 c_1 \,x^{3}-12 c_1 \,x^{2}+6 c_1 x -c_1 \right ) \textit {\_Z}^{4}-\textit {\_Z} \right )\right )}{2} \]

✓ Mathematica. Time used: 60.165 (sec). Leaf size: 4937

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

Too large to display

✗ Sympy

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

Timed Out