23.1.482 problem 472

Internal problem ID [5089]
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 : 472
Date solved : Tuesday, September 30, 2025 at 11:34:49 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3+2 x -2 y\right ) y^{\prime }&=1+6 x -2 y \end{align*}

✓ Maple. Time used: 0.187 (sec). Leaf size: 33

ode:=(3+2*x-2*y(x))*diff(y(x),x) = 1+6*x-2*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\sqrt {1-8 \left (x -\frac {1}{2}\right )^{2} c_1^{2}}+\left (2 x +3\right ) c_1}{2 c_1} \]

✓ Mathematica. Time used: 0.08 (sec). Leaf size: 67

ode=(3+2*x-2*y[x])*D[y[x],x]==1+6*x-2*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{2} i \sqrt {8 x^2-8 x-9-4 c_1}+x+\frac {3}{2}\\ y(x)&\to \frac {1}{2} i \sqrt {8 x^2-8 x-9-4 c_1}+x+\frac {3}{2} \end{align*}

✓ Sympy. Time used: 1.604 (sec). Leaf size: 44

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x + (2*x - 2*y(x) + 3)*Derivative(y(x), x) + 2*y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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