88.7.4 problem 4

Internal problem ID [23999]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 41
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:51:10 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +2 y-3+\left (1-2 y+2 x \right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.169 (sec). Leaf size: 21

ode:=2*x+2*y(x)-3+(1-2*y(x)+2*x)*diff(y(x),x) = 0; 
ic:=[y(1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = x +\frac {1}{2}+\frac {\sqrt {8 x^{2}-8 x +1}}{2} \]

✓ Mathematica. Time used: 0.087 (sec). Leaf size: 30

ode=( 2*x+2*y[x]-3 )+( 1-2*y[x]+2*x )*D[y[x],{x,1}]==0; 
ic={y[1]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.565 (sec). Leaf size: 22

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

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