81.15.3 problem 19-3

Internal problem ID [21711]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 19. Change of variables. Page 483
Problem number : 19-3
Date solved : Thursday, October 02, 2025 at 08:00:36 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +2 y+3+\left (2 x +4 y-1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 41

ode:=x+2*y(x)+3+(2*x+4*y(x)-1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {x}{2}+\frac {1}{4}-\frac {\sqrt {28 c_1 -28 x +1}}{4} \\ y &= -\frac {x}{2}+\frac {1}{4}+\frac {\sqrt {28 c_1 -28 x +1}}{4} \\ \end{align*}

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 55

ode=(x+2*y[x]+3)+(2*x+4*y[x]-1)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{4} \left (-2 x-\sqrt {-28 x+1+16 c_1}+1\right )\\ y(x)&\to \frac {1}{4} \left (-2 x+\sqrt {-28 x+1+16 c_1}+1\right ) \end{align*}

✓ Sympy. Time used: 0.695 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (2*x + 4*y(x) - 1)*Derivative(y(x), x) + 2*y(x) + 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {x}{2} - \frac {\sqrt {C_{1} - 28 x}}{4} + \frac {1}{4}, \ y{\left (x \right )} = - \frac {x}{2} + \frac {\sqrt {C_{1} - 28 x}}{4} + \frac {1}{4}\right ] \]