23.1.463 problem 453

Internal problem ID [5070]
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 : 453
Date solved : Tuesday, September 30, 2025 at 11:32:24 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (5-2 x -y\right ) y^{\prime }+4-x -2 y&=0 \end{align*}

✓ Maple. Time used: 0.125 (sec). Leaf size: 32

ode:=(5-2*x-y(x))*diff(y(x),x)+4-x-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\sqrt {3 \left (-2+x \right )^{2} c_1^{2}+1}+\left (-2 x +5\right ) c_1}{c_1} \]

✓ Mathematica. Time used: 0.09 (sec). Leaf size: 53

ode=(5-2*x-y[x])*D[y[x],x]+4-x-2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {3 x^2-12 x+25+c_1}-2 x+5\\ y(x)&\to \sqrt {3 x^2-12 x+25+c_1}-2 x+5 \end{align*}

✓ Sympy. Time used: 1.248 (sec). Leaf size: 41

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

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