89.10.14 problem 14

Internal problem ID [24507]
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 77
Problem number : 14
Date solved : Thursday, October 02, 2025 at 10:43:50 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 21

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

\[ y = -3 x -3 \operatorname {LambertW}\left (-\frac {c_1 \,{\mathrm e}^{-\frac {7}{3}-\frac {2 x}{3}}}{3}\right )-7 \]

✓ Mathematica. Time used: 2.215 (sec). Leaf size: 35

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

\begin{align*} y(x)&\to -3 W\left (-e^{-\frac {2 x}{3}-1+c_1}\right )-3 x-7\\ y(x)&\to -3 x-7 \end{align*}

✓ Sympy. Time used: 2.211 (sec). Leaf size: 107

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

\[ \left [ y{\left (x \right )} = - 3 x - 3 W\left (\frac {\sqrt [3]{C_{1} e^{- 2 x}}}{3 e^{\frac {7}{3}}}\right ) - 7, \ y{\left (x \right )} = - 3 x - 3 W\left (- \frac {\sqrt [3]{C_{1} e^{- 2 x}} \left (1 - \sqrt {3} i\right )}{6 e^{\frac {7}{3}}}\right ) - 7, \ y{\left (x \right )} = - 3 x - 3 W\left (- \frac {\sqrt [3]{C_{1} e^{- 2 x}} \left (1 + \sqrt {3} i\right )}{6 e^{\frac {7}{3}}}\right ) - 7\right ] \]