44.4.4 problem 4

Internal problem ID [9139]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page 20
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 06:06:40 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out