29.18.3 problem 479

Internal problem ID [5077]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 479
Date solved : Tuesday, March 04, 2025 at 07:51:35 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 21

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

\[ y \left (x \right ) = -\frac {x}{3}-\frac {\operatorname {LambertW}\left (-\frac {c_{1} {\mathrm e}^{\frac {4 x}{3}+\frac {5}{3}}}{3}\right )}{2}+\frac {5}{6} \]

✓ Mathematica. Time used: 4.127 (sec). Leaf size: 43

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

\begin{align*} y(x)\to \frac {1}{6} \left (-3 W\left (-e^{\frac {4 x}{3}-1+c_1}\right )-2 x+5\right ) \\ y(x)\to \frac {1}{6} (5-2 x) \\ \end{align*}

✓ Sympy. Time used: 3.066 (sec). Leaf size: 107

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

\[ \left [ y{\left (x \right )} = - \frac {x}{3} - \frac {W\left (\frac {\sqrt [3]{C_{1} e^{4 x}} e^{\frac {5}{3}}}{3}\right )}{2} + \frac {5}{6}, \ y{\left (x \right )} = - \frac {x}{3} - \frac {W\left (- \frac {\sqrt [3]{C_{1} e^{4 x}} \left (1 - \sqrt {3} i\right ) e^{\frac {5}{3}}}{6}\right )}{2} + \frac {5}{6}, \ y{\left (x \right )} = - \frac {x}{3} - \frac {W\left (- \frac {\sqrt [3]{C_{1} e^{4 x}} \left (1 + \sqrt {3} i\right ) e^{\frac {5}{3}}}{6}\right )}{2} + \frac {5}{6}\right ] \]