62.12.11 problem Ex 12

Internal problem ID [12786]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
Problem number : Ex 12
Date solved : Monday, March 31, 2025 at 07:07:25 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.223 (sec). Leaf size: 115

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

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

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

ode=(x-2*y[x]+5)+(2*x-y[x]+4)*D[y[x],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