23.1.516 problem 506

Internal problem ID [5123]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 506
Date solved : Tuesday, September 30, 2025 at 11:42:55 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (a_{2} +b x +c_{2} y\right ) y^{\prime }+a_{1} +b_{1} x +b y&=0 \end{align*}

✓ Maple. Time used: 0.095 (sec). Leaf size: 81

ode:=(a__2+b*x+c__2*y(x))*diff(y(x),x)+a__1+b__1*x+b*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\sqrt {\left (b^{2}-b_{1} c_{2} \right ) \left (\left (-b_{1} x -a_{1} \right ) c_{2} +b \left (b x +a_{2} \right )\right )^{2} c_3^{2}+c_{2}}+\left (b_{1} \left (b x +a_{2} \right ) c_{2} -x \,b^{3}-a_{2} b^{2}\right ) c_3}{c_{2} c_3 \left (b^{2}-b_{1} c_{2} \right )} \]

✓ Mathematica. Time used: 17.833 (sec). Leaf size: 106

ode=(a2+b*x+c2*y[x])*D[y[x],x]+(a1+b1*x+b*y[x])==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\frac {\sqrt {-x (2 \text {a1}+\text {b1} x)+\frac {(\text {a2}+b x)^2}{\text {c2}}+\text {c2} c_1}}{\sqrt {\frac {1}{\text {c2}}}}+\text {a2}+b x}{\text {c2}}\\ y(x)&\to -\frac {\text {a2}+b x}{\text {c2}}+\sqrt {\frac {1}{\text {c2}}} \sqrt {-x (2 \text {a1}+\text {b1} x)+\frac {(\text {a2}+b x)^2}{\text {c2}}+\text {c2} c_1} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a2 = symbols("a2") 
b = symbols("b") 
c2 = symbols("c2") 
a1 = symbols("a1") 
b1 = symbols("b1") 
y = Function("y") 
ode = Eq(a1 + b*y(x) + b1*x + (a2 + b*x + c2*y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(-a1 - b*y(x) - b1*x)/(a2 + b*x + c2*y(x)) + Derivative(y(x), x