29.16.12 problem 455

Internal problem ID [5053]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 455
Date solved : Tuesday, March 04, 2025 at 07:48:35 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (1+5 x -y\right ) y^{\prime }+5+x -5 y&=0 \end{align*}

✓ Maple. Time used: 0.145 (sec). Leaf size: 242

ode:=(1+5*x-y(x))*diff(y(x),x)+5+x-5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {i \left (1-{\left (6 \sqrt {3}\, x \sqrt {\frac {27 c_{1} x^{2}+2 x}{c_{1}}}\, c_{1}^{2}+54 c_{1}^{2} x^{2}+18 c_{1} x +1\right )}^{{2}/{3}}+12 c_{1} x \right ) \sqrt {3}+6 \left (\left (2-{\left (6 \sqrt {3}\, x \sqrt {\frac {27 c_{1} x^{2}+2 x}{c_{1}}}\, c_{1}^{2}+54 c_{1}^{2} x^{2}+18 c_{1} x +1\right )}^{{1}/{3}}\right ) x +{\left (6 \sqrt {3}\, x \sqrt {\frac {27 c_{1} x^{2}+2 x}{c_{1}}}\, c_{1}^{2}+54 c_{1}^{2} x^{2}+18 c_{1} x +1\right )}^{{1}/{3}}\right ) c_{1} +{\left ({\left (6 \sqrt {3}\, x \sqrt {\frac {27 c_{1} x^{2}+2 x}{c_{1}}}\, c_{1}^{2}+54 c_{1}^{2} x^{2}+18 c_{1} x +1\right )}^{{1}/{3}}-1\right )}^{2}}{6 {\left (6 \sqrt {3}\, x \sqrt {\frac {27 c_{1} x^{2}+2 x}{c_{1}}}\, c_{1}^{2}+54 c_{1}^{2} x^{2}+18 c_{1} x +1\right )}^{{1}/{3}} c_{1}} \]

✓ Mathematica. Time used: 60.05 (sec). Leaf size: 925

ode=(1+5 x-y[x])D[y[x],x]+5+x-5 y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (5*x - y(x) + 1)*Derivative(y(x), x) - 5*y(x) + 5,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out