21.1.6 problem 6

Internal problem ID [4082]
Book : Differential equations, Shepley L. Ross, 1964
Section : 2.4, page 55
Problem number : 6
Date solved : Sunday, March 30, 2025 at 02:16:41 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 23

ode:=3*x-y(x)+1-(6*x-2*y(x)-3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 3.076 (sec). Leaf size: 35

ode=(3*x-y[x]+1)-(6*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}{2} W\left (-e^{5 x-1+c_1}\right )+3 x-2 \\ y(x)\to 3 x-2 \\ \end{align*}

✓ Sympy. Time used: 0.954 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x - (6*x - 2*y(x) - 3)*Derivative(y(x), x) - y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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