89.8.4 problem 4

Internal problem ID [24464]
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 66
Problem number : 4
Date solved : Thursday, October 02, 2025 at 10:39:26 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x -4 y-3-\left (x -6 y-5\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 1.357 (sec). Leaf size: 31

ode:=x-4*y(x)-3-(x-6*y(x)-5)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\sqrt {9+\left (-8 x -8\right ) c_1}-3+\left (4 x -4\right ) c_1}{8 c_1} \]

✓ Mathematica. Time used: 60.082 (sec). Leaf size: 1177

ode=( x-4*y[x]-3 )-( x-6*y[x]-5 )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✓ Sympy. Time used: 1.834 (sec). Leaf size: 58

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x - (x - 6*y(x) - 5)*Derivative(y(x), x) - 4*y(x) - 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {3 C_{1}}{8} + \frac {x}{2} + \frac {\sqrt {C_{1} \left (9 C_{1} - 8 x - 8\right )}}{8} - \frac {1}{2}, \ y{\left (x \right )} = - \frac {3 C_{1}}{8} + \frac {x}{2} - \frac {\sqrt {C_{1} \left (9 C_{1} - 8 x - 8\right )}}{8} - \frac {1}{2}\right ] \]