23.1.498 problem 488

Internal problem ID [5105]
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 : 488
Date solved : Tuesday, September 30, 2025 at 11:37:27 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (5+2 x -4 y\right ) y^{\prime }&=3+x -2 y \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 41

ode:=(5+2*x-4*y(x))*diff(y(x),x) = 3+x-2*y(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {x}{2}+\frac {5}{4}-\frac {\sqrt {4 c_1 -4 x +25}}{4} \\ y &= \frac {x}{2}+\frac {5}{4}+\frac {\sqrt {4 c_1 -4 x +25}}{4} \\ \end{align*}

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 61

ode=(5+2*x-4*y[x])*D[y[x],x]==3+x-2*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{4} \left (2 x-i \sqrt {4 x-25-16 c_1}+5\right )\\ y(x)&\to \frac {1}{4} \left (2 x+i \sqrt {4 x-25-16 c_1}+5\right ) \end{align*}

✓ Sympy. Time used: 0.690 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + (2*x - 4*y(x) + 5)*Derivative(y(x), x) + 2*y(x) - 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {x}{2} - \frac {\sqrt {C_{1} - 4 x}}{4} + \frac {5}{4}, \ y{\left (x \right )} = \frac {x}{2} + \frac {\sqrt {C_{1} - 4 x}}{4} + \frac {5}{4}\right ] \]