88.12.10 problem 12

Internal problem ID [24066]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Miscellaneous Exercises at page 55
Problem number : 12
Date solved : Thursday, October 02, 2025 at 09:56:51 PM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

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

With initial conditions

\begin{align*} y \left (4\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.076 (sec). Leaf size: 20

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

\[ y = 3 x -\frac {4}{3}-\frac {\operatorname {LambertW}\left (32 \,{\mathrm e}^{9 x -4}\right )}{3} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to \frac {1}{3} \left (-W\left (32 e^{9 x-4}\right )+9 x-4\right ) \end{align*}

✓ Sympy. Time used: 0.567 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = 3 x - \frac {W\left (32 e^{9 x - 4}\right )}{3} - \frac {4}{3} \]