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 : Sunday, March 30, 2025 at 06:32:01 AM
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: 0.228 (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);
 

\[ y = -\frac {\left (i \sqrt {3}-1\right ) \left (3 \sqrt {3}\, \sqrt {27 c_1^{2} \left (1+x \right )^{2}-1}+27 \left (1+x \right ) c_1 \right )^{{2}/{3}}-3 i \sqrt {3}-3+6 \left (3 \sqrt {3}\, \sqrt {27 c_1^{2} \left (1+x \right )^{2}-1}+27 c_1 x +27 c_1 \right )^{{1}/{3}} \left (x -1\right ) c_1}{6 \left (3 \sqrt {3}\, \sqrt {27 c_1^{2} \left (1+x \right )^{2}-1}+27 \left (1+x \right ) c_1 \right )^{{1}/{3}} c_1} \]

✓ 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