81.3.36 problem 36

Internal problem ID [18575]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 36
Date solved : Thursday, March 13, 2025 at 12:24:15 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (6 x -4 y+1\right ) y^{\prime }&=3 x -2 y+1 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 21

ode:=(6*x-4*y(x)+1)*diff(y(x),x) = 3*x-2*y(x)+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {3 x}{2}-\frac {\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{1+8 x}\right )}{8}+\frac {1}{8} \]

✓ Mathematica. Time used: 3.973 (sec). Leaf size: 41

ode=(6*x-4*y[x]+1)*D[y[x],x]==3*x-2*y[x]+1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{8} \left (-W\left (-e^{8 x-1+c_1}\right )+12 x+1\right ) \\ y(x)\to \frac {3 x}{2}+\frac {1}{8} \\ \end{align*}

✓ Sympy. Time used: 1.038 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x + (6*x - 4*y(x) + 1)*Derivative(y(x), x) + 2*y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {3 x}{2} - \frac {W\left (C_{1} e^{8 x + 1}\right )}{8} + \frac {1}{8} \]