89.7.1 problem 1

Internal problem ID [24432]
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 61
Problem number : 1
Date solved : Thursday, October 02, 2025 at 10:29:33 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 21

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

\[ y = \frac {3 x}{2}-\frac {2 \operatorname {LambertW}\left (-\frac {c_1 \,{\mathrm e}^{\frac {11}{4}+\frac {25 x}{4}}}{4}\right )}{5}+\frac {11}{10} \]

✓ Mathematica. Time used: 2.42 (sec). Leaf size: 43

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

\begin{align*} y(x)&\to \frac {1}{10} \left (-4 W\left (-e^{\frac {25 x}{4}-1+c_1}\right )+15 x+11\right )\\ y(x)&\to \frac {3 x}{2}+\frac {11}{10} \end{align*}

✓ Sympy. Time used: 2.525 (sec). Leaf size: 136

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

\[ \left [ y{\left (x \right )} = \frac {3 x}{2} - \frac {2 W\left (- \frac {\sqrt [4]{C_{1} e^{25 x}} e^{\frac {11}{4}}}{4}\right )}{5} + \frac {11}{10}, \ y{\left (x \right )} = \frac {3 x}{2} - \frac {2 W\left (\frac {\sqrt [4]{C_{1} e^{25 x}} e^{\frac {11}{4}}}{4}\right )}{5} + \frac {11}{10}, \ y{\left (x \right )} = \frac {3 x}{2} - \frac {2 W\left (- \frac {i \sqrt [4]{C_{1} e^{25 x}} e^{\frac {11}{4}}}{4}\right )}{5} + \frac {11}{10}, \ y{\left (x \right )} = \frac {3 x}{2} - \frac {2 W\left (\frac {i \sqrt [4]{C_{1} e^{25 x}} e^{\frac {11}{4}}}{4}\right )}{5} + \frac {11}{10}\right ] \]