23.1.509 problem 499

Internal problem ID [5116]
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 : 499
Date solved : Tuesday, September 30, 2025 at 11:40:55 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (8+5 x -12 y\right ) y^{\prime }&=3+2 x -5 y \end{align*}

✓ Maple. Time used: 0.177 (sec). Leaf size: 32

ode:=(8+5*x-12*y(x))*diff(y(x),x) = 3+2*x-5*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\sqrt {\left (x +4\right )^{2} c_1^{2}+24}+\left (5 x +8\right ) c_1}{12 c_1} \]

✓ Mathematica. Time used: 0.082 (sec). Leaf size: 77

ode=(8+5*x-12*y[x])*D[y[x],x]==3+2*x-5*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{12} \left (-i \sqrt {-x^2-8 x-16 (4+9 c_1)}+5 x+8\right )\\ y(x)&\to \frac {1}{12} \left (i \sqrt {-x^2-8 x-16 (4+9 c_1)}+5 x+8\right ) \end{align*}

✓ Sympy. Time used: 1.424 (sec). Leaf size: 48

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x + (5*x - 12*y(x) + 8)*Derivative(y(x), x) + 5*y(x) - 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {5 x}{12} - \frac {\sqrt {C_{1} + x^{2} + 8 x}}{12} + \frac {2}{3}, \ y{\left (x \right )} = \frac {5 x}{12} + \frac {\sqrt {C_{1} + x^{2} + 8 x}}{12} + \frac {2}{3}\right ] \]