32.6.8 problem Exercise 12.8, page 103

Internal problem ID [5873]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.8, page 103
Date solved : Tuesday, March 04, 2025 at 11:50:38 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2&=0 \end{align*}

✓ Maple. Time used: 0.954 (sec). Leaf size: 32

ode:=(3*x+2*y(x)+1)*diff(y(x),x)+4*x+3*y(x)+2 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.141 (sec). Leaf size: 61

ode=(3*x+2*y[x]+1)*D[y[x],x]+(4*x+3*y[x]+2)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 2.056 (sec). Leaf size: 49

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x + (3*x + 2*y(x) + 1)*Derivative(y(x), x) + 3*y(x) + 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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