6.9.46 problem 39 part(d)

Internal problem ID [1802]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page 253
Problem number : 39 part(d)
Date solved : Tuesday, September 30, 2025 at 05:19:35 AM
CAS classification : [_rational, _Riccati]

\begin{align*} \left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-\left (3 x +2\right ) y-6 x +8&=0 \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 31

ode:=(3*x-1)*(diff(y(x),x)+y(x)^2)-(3*x+2)*y(x)-6*x+8 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-c_1 x +2 \,{\mathrm e}^{3 x -1}+c_1}{c_1 x +{\mathrm e}^{3 x -1}} \]

✓ Mathematica. Time used: 0.282 (sec). Leaf size: 41

ode=(3*x-1)*(D[y[x],x]+y[x]^2)-(3*x+2)*y[x]-6*x+8==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 \left (-e x+c_1 e^{3 x}+e\right )}{2 e x+c_1 e^{3 x}}\\ y(x)&\to 2 \end{align*}

✓ Sympy. Time used: 0.287 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x + (3*x - 1)*(y(x)**2 + Derivative(y(x), x)) - (3*x + 2)*y(x) + 8,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {- C_{1} x + C_{1} - 2 e^{3 x}}{C_{1} x - e^{3 x}} \]