89.9.5 problem 5

Internal problem ID [24485]
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 72
Problem number : 5
Date solved : Thursday, October 02, 2025 at 10:42:20 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 55

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

\begin{align*} y &= -\frac {x}{4}+\frac {1}{2}-\frac {\sqrt {x^{2}-8 \ln \left (x \right )-8 c_1 -4 x +4}}{4} \\ y &= -\frac {x}{4}+\frac {1}{2}+\frac {\sqrt {x^{2}-8 \ln \left (x \right )-8 c_1 -4 x +4}}{4} \\ \end{align*}

✓ Mathematica. Time used: 0.338 (sec). Leaf size: 88

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

\begin{align*} y(x)&\to \frac {1}{4} \left (-\sqrt {\frac {1}{x}} \sqrt {x \left (x^2-4 x-8 \log (x)+4+16 c_1\right )}-x+2\right )\\ y(x)&\to \frac {1}{4} \left (\sqrt {\frac {1}{x}} \sqrt {x \left (x^2-4 x-8 \log (x)+4+16 c_1\right )}-x+2\right ) \end{align*}

✗ Sympy

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

Timed Out