29.16.6 problem 449

Internal problem ID [5047]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 449
Date solved : Tuesday, March 04, 2025 at 07:46:34 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (4+2 x -y\right ) y^{\prime }+5+x -2 y&=0 \end{align*}

✓ Maple. Time used: 1.097 (sec). Leaf size: 115

ode:=(4+2*x-y(x))*diff(y(x),x)+5+x-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {\frac {1}{2}+\frac {\left (1-i \sqrt {3}\right ) \left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +1\right )^{2}-1}+27 \left (x +1\right ) c_{1} \right )^{{2}/{3}}}{6}+\frac {i \sqrt {3}}{2}-\left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +1\right )^{2}-1}+27 c_{1} x +27 c_{1} \right )^{{1}/{3}} \left (x -1\right ) c_{1}}{\left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +1\right )^{2}-1}+27 \left (x +1\right ) c_{1} \right )^{{1}/{3}} c_{1}} \]

✓ Mathematica. Time used: 60.186 (sec). Leaf size: 1601

ode=(4+2 x-y[x])D[y[x],x]+5+x-2 y[x]==0; 
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(x + (2*x - y(x) + 4)*Derivative(y(x), x) - 2*y(x) + 5,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out