40.2.20 problem 45

Internal problem ID [6598]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 45
Date solved : Sunday, March 30, 2025 at 11:11:35 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.020 (sec). Leaf size: 21

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

\[ y = -\frac {3 x}{2}-\frac {2 \operatorname {LambertW}\left (-\frac {c_1 \,{\mathrm e}^{\frac {1}{4}-\frac {25 x}{4}}}{4}\right )}{5}+\frac {1}{10} \]

✓ Mathematica. Time used: 4.124 (sec). Leaf size: 43

ode=(3*x+2*y[x]+1)-(3*x+2*y[x]-1)*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+1\right ) \\ y(x)\to \frac {1}{10}-\frac {3 x}{2} \\ \end{align*}

✓ Sympy. Time used: 3.903 (sec). Leaf size: 136

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

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