85.13.8 problem 8

Internal problem ID [22514]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 40
Problem number : 8
Date solved : Thursday, October 02, 2025 at 08:44:44 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +3 y+4&=\left (4 x +6 y+1\right ) y^{\prime } \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 23

ode:=2*x+3*y(x)+4 = (4*x+6*y(x)+1)*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\operatorname {LambertW}\left (-\frac {2 \,{\mathrm e}^{-\frac {7 x}{3}-\frac {4}{3}+\frac {7 c_1}{3}}}{3}\right )}{2}-\frac {2 x}{3}-\frac {2}{3} \]

✓ Mathematica. Time used: 2.396 (sec). Leaf size: 42

ode=(2*x+3*y[x]+4)==(4*x+6*y[x]+1)*D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{6} \left (-4 (x+1)-3 W\left (-e^{-\frac {7 x}{3}-1+c_1}\right )\right )\\ y(x)&\to -\frac {2}{3} (x+1) \end{align*}

✓ Sympy. Time used: 2.452 (sec). Leaf size: 119

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x - (4*x + 6*y(x) + 1)*Derivative(y(x), x) + 3*y(x) + 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {2 x}{3} - \frac {W\left (\frac {2 \sqrt [3]{C_{1} e^{- 7 x}}}{3 e^{\frac {4}{3}}}\right )}{2} - \frac {2}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - \frac {W\left (- \frac {\sqrt [3]{C_{1} e^{- 7 x}} \left (1 - \sqrt {3} i\right )}{3 e^{\frac {4}{3}}}\right )}{2} - \frac {2}{3}, \ y{\left (x \right )} = - \frac {2 x}{3} - \frac {W\left (- \frac {\sqrt [3]{C_{1} e^{- 7 x}} \left (1 + \sqrt {3} i\right )}{3 e^{\frac {4}{3}}}\right )}{2} - \frac {2}{3}\right ] \]