74.3.3 problem 3

Internal problem ID [19833]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 29. Problems at page 81
Problem number : 3
Date solved : Thursday, October 02, 2025 at 04:46:20 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.131 (sec). Leaf size: 90

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

\[ y = \frac {-\sqrt {-64 \left (a c -\frac {b^{2}}{4}\right ) \left (\left (a x -\frac {g}{2}\right ) c -\frac {b \left (b x +e \right )}{4}\right )^{2} c_1^{2}+4 c}+\left (-4 a b c x +b^{3} x -4 a c e +b^{2} e \right ) c_1}{8 \left (a c -\frac {b^{2}}{4}\right ) c_1 c} \]

✓ Mathematica. Time used: 20.463 (sec). Leaf size: 132

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

\begin{align*} y(x)&\to -\frac {\frac {\sqrt {\frac {4 c x (g-a x)+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 (g-a x)+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