67.5.2 problem 6.1 (b)

Internal problem ID [16400]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.1 (b)
Date solved : Thursday, October 02, 2025 at 01:27:50 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 39

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

\begin{align*} y &= \frac {3 x}{2}-\frac {\sqrt {{\mathrm e}^{-4 x} c_1 -1}}{2} \\ y &= \frac {3 x}{2}+\frac {\sqrt {{\mathrm e}^{-4 x} c_1 -1}}{2} \\ \end{align*}

✓ Mathematica. Time used: 10.931 (sec). Leaf size: 78

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

\begin{align*} y(x)&\to \frac {1}{2} \left (3 x-\frac {\sqrt {e^{4 x}-4 c_1}}{\sqrt {-e^{4 x}}}\right )\\ y(x)&\to \frac {1}{2} \left (3 x+\frac {\sqrt {e^{4 x}-4 c_1}}{\sqrt {-e^{4 x}}}\right ) \end{align*}

✓ Sympy. Time used: 1.240 (sec). Leaf size: 41

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

\[ \left [ y{\left (x \right )} = \frac {3 x}{2} - \frac {\sqrt {C_{1} e^{- 4 x} - 1}}{2}, \ y{\left (x \right )} = \frac {3 x}{2} + \frac {\sqrt {C_{1} e^{- 4 x} - 1}}{2}\right ] \]