75.3.32 problem 33

Internal problem ID [19936]
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 : 33
Date solved : Thursday, October 02, 2025 at 05:04:04 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x -3 y+4\right ) y^{\prime }&=2 x -6 y+7 \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 21

ode:=(x-3*y(x)+4)*diff(y(x),x) = 2*x-6*y(x)+7; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x}{3}-\frac {\operatorname {LambertW}\left (-\frac {c_1 \,{\mathrm e}^{\frac {17}{3}-\frac {25 x}{3}}}{3}\right )}{5}+\frac {17}{15} \]

✓ Mathematica. Time used: 2.496 (sec). Leaf size: 43

ode=(x-3*y[x]+4)*D[y[x],x]==2*x-6*y[x]+7; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{15} \left (-3 W\left (-e^{-\frac {25 x}{3}-1+c_1}\right )+5 x+17\right )\\ y(x)&\to \frac {1}{15} (5 x+17) \end{align*}

✓ Sympy. Time used: 2.380 (sec). Leaf size: 105

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x + (x - 3*y(x) + 4)*Derivative(y(x), x) + 6*y(x) - 7,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {x}{3} - \frac {W\left (\frac {\sqrt [3]{C_{1} e^{- 25 x}} e^{\frac {17}{3}}}{3}\right )}{5} + \frac {17}{15}, \ y{\left (x \right )} = \frac {x}{3} - \frac {W\left (\frac {\sqrt [3]{C_{1} e^{- 25 x}} \left (-1 + \sqrt {3} i\right ) e^{\frac {17}{3}}}{6}\right )}{5} + \frac {17}{15}, \ y{\left (x \right )} = \frac {x}{3} - \frac {W\left (- \frac {\sqrt [3]{C_{1} e^{- 25 x}} \left (1 + \sqrt {3} i\right ) e^{\frac {17}{3}}}{6}\right )}{5} + \frac {17}{15}\right ] \]