82.5.4 problem Ex. 4

Internal problem ID [18661]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 20
Problem number : Ex. 4
Date solved : Thursday, March 13, 2025 at 12:31:30 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.134 (sec). Leaf size: 90

ode:=2*a*x+b*y(x)+g+(2*c*y(x)+b*x+e)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {-\sqrt {-64 \left (a c -\frac {b^{2}}{4}\right ) \left (\left (a x +\frac {g}{2}\right ) c -\frac {b \left (b x +e \right )}{4}\right )^{2} c_{1}^{2}+4 c}+\left (-4 a b c x +b^{3} x -4 a c e +b^{2} e \right ) c_{1}}{8 c \left (a c -\frac {b^{2}}{4}\right ) c_{1}} \]

✓ Mathematica. Time used: 16.969 (sec). Leaf size: 130

ode=(2*a*x+b*y[x]+g)+(2*c*y[x]+b*x+e)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {\frac {\sqrt {\frac {-4 c x (a x+g)+b^2 x^2+2 b e x+4 c^2 c_1+e^2}{c}}}{\sqrt {\frac {1}{c}}}+b x+e}{2 c} \\ y(x)\to -\frac {-\frac {\sqrt {\frac {-4 c x (a x+g)+b^2 x^2+2 b e x+4 c^2 c_1+e^2}{c}}}{\sqrt {\frac {1}{c}}}+b x+e}{2 c} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
e = symbols("e") 
g = symbols("g") 
y = Function("y") 
ode = Eq(2*a*x + b*y(x) + g + (b*x + 2*c*y(x) + e)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(-2*a*x - b*y(x) - g)/(b*x + 2*c*y(x) + e) + Derivative(y(x), x) cannot be solved by the factorable group method