89.7.24 problem 23

Internal problem ID [24455]
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 : 23
Date solved : Thursday, October 02, 2025 at 10:37:01 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 12 x +4 y-8-\left (3 x +y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.082 (sec). Leaf size: 20

ode:=12*x+4*y(x)-8-(3*x+y(x))*diff(y(x),x) = 0; 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -3 x +\frac {8 \operatorname {LambertW}\left (\frac {13 \,{\mathrm e}^{-\frac {9}{2}+\frac {49 x}{8}}}{8}\right )}{7}+\frac {8}{7} \]

✓ Mathematica. Time used: 2.173 (sec). Leaf size: 32

ode=4*(3*x+y[x]-2 )-(3*x+y[x])*D[y[x],x]==0; 
ic={y[1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {8}{7} W\left (\frac {13}{8} e^{\frac {49 x}{8}-\frac {9}{2}}\right )-3 x+\frac {8}{7} \end{align*}

✓ Sympy. Time used: 12.405 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*x - (3*x + y(x))*Derivative(y(x), x) + 4*y(x) - 8,0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - 3 x + \frac {8 W\left (\frac {13 \sqrt [8]{e^{49 x}}}{8 e^{\frac {9}{2}}}\right )}{7} + \frac {8}{7} \]