89.8.5 problem 5

Internal problem ID [24465]
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 : 5
Date solved : Thursday, October 02, 2025 at 10:39:49 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +3 y-5+\left (3 x -y-2\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.144 (sec). Leaf size: 32

ode:=2*x+3*y(x)-5+(3*x-y(x)-2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\sqrt {11 \left (x -1\right )^{2} c_1^{2}+1}+\left (3 x -2\right ) c_1}{c_1} \]

✓ Mathematica. Time used: 0.082 (sec). Leaf size: 63

ode=( 2*x+3*y[x]-5)+( 3*x-y[x]-2 )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -i \sqrt {-11 x^2+22 x-4-c_1}+3 x-2\\ y(x)&\to i \sqrt {-11 x^2+22 x-4-c_1}+3 x-2 \end{align*}

✓ Sympy. Time used: 1.268 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (3*x - y(x) - 2)*Derivative(y(x), x) + 3*y(x) - 5,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = 3 x - \sqrt {C_{1} + 11 x^{2} - 22 x} - 2, \ y{\left (x \right )} = 3 x + \sqrt {C_{1} + 11 x^{2} - 22 x} - 2\right ] \]