89.10.26 problem 26

Internal problem ID [24519]
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 : 26
Date solved : Thursday, October 02, 2025 at 10:44:58 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 4 x +3 y-7+\left (4 x +3 y+1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 21

ode:=4*x+3*y(x)-7+(4*x+3*y(x)+1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {4 x}{3}-8 \operatorname {LambertW}\left (-\frac {c_1 \,{\mathrm e}^{-\frac {25}{24}-\frac {x}{24}}}{24}\right )-\frac {25}{3} \]

✓ Mathematica. Time used: 2.231 (sec). Leaf size: 43

ode=( 4*x+3*y[x]-7)+( 4*x+3*y[x]+1 )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -8 W\left (-e^{-\frac {x}{24}-1+c_1}\right )-\frac {4 x}{3}-\frac {25}{3}\\ y(x)&\to \frac {1}{3} (-4 x-25) \end{align*}

✓ Sympy. Time used: 129.290 (sec). Leaf size: 976

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x + (4*x + 3*y(x) + 1)*Derivative(y(x), x) + 3*y(x) - 7,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]