89.7.8 problem 8

Internal problem ID [24439]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 61
Problem number : 8
Date solved : Thursday, October 02, 2025 at 10:32:15 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

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

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

\begin{align*} y &= -\frac {x}{2}+\frac {3}{4}-\frac {\sqrt {4 c_1 -4 x +9}}{4} \\ y &= -\frac {x}{2}+\frac {3}{4}+\frac {\sqrt {4 c_1 -4 x +9}}{4} \\ \end{align*}

✓ Mathematica. Time used: 0.067 (sec). Leaf size: 55

ode=(x+2*y[x]-1)+( 2*x+4*y[x]-3 )*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 {-4 x+9+16 c_1}+3\right )\\ y(x)&\to \frac {1}{4} \left (-2 x+\sqrt {-4 x+9+16 c_1}+3\right ) \end{align*}

✓ Sympy. Time used: 0.666 (sec). Leaf size: 37

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

\[ \left [ y{\left (x \right )} = - \frac {x}{2} - \frac {\sqrt {C_{1} - 4 x}}{4} + \frac {3}{4}, \ y{\left (x \right )} = - \frac {x}{2} + \frac {\sqrt {C_{1} - 4 x}}{4} + \frac {3}{4}\right ] \]