89.8.2 problem 2

Internal problem ID [24462]
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 : 2
Date solved : Thursday, October 02, 2025 at 10:39:05 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x -4 y-9+\left (4 x +y-2\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 31

ode:=x-4*y(x)-9+(4*x+y(x)-2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -2-\tan \left (\operatorname {RootOf}\left (-8 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x -1\right )+2 c_1 \right )\right ) \left (x -1\right ) \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 66

ode=( x-4*y[x]-9 )+( 4*x+y[x]-2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [256 \arctan \left (\frac {4 y(x)-x+9}{y(x)+4 x-2}\right )+32 \log \left (\frac {x^2+y(x)^2+4 y(x)-2 x+5}{17 (x-1)^2}\right )+64 \log (x-1)+17 c_1=0,y(x)\right ] \]

✓ Sympy. Time used: 2.136 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (4*x + y(x) - 2)*Derivative(y(x), x) - 4*y(x) - 9,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \log {\left (x - 1 \right )} = C_{1} - \log {\left (\sqrt {1 + \frac {\left (y{\left (x \right )} + 2\right )^{2}}{\left (x - 1\right )^{2}}} \right )} - 4 \operatorname {atan}{\left (\frac {y{\left (x \right )} + 2}{x - 1} \right )} \]