81.3.34 problem 34

Internal problem ID [18573]
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 : 34
Date solved : Thursday, March 13, 2025 at 12:24:10 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (5 x -2 y+7\right ) y^{\prime }&=10 x -4 y+6 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 21

ode:=(5*x-2*y(x)+7)*diff(y(x),x) = 10*x-4*y(x)+6; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {5 x}{2}+8 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {x}{16}-\frac {23}{16}}}{16}\right )+\frac {23}{2} \]

✓ Mathematica. Time used: 3.209 (sec). Leaf size: 43

ode=(5*x-2*y[x]+7)*D[y[x],x]==10*x-4*y[x]+6; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to 8 W\left (-e^{-\frac {x}{16}-1+c_1}\right )+\frac {5 x}{2}+\frac {23}{2} \\ y(x)\to \frac {1}{2} (5 x+23) \\ \end{align*}

✓ Sympy. Time used: 85.225 (sec). Leaf size: 680

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-10*x + (5*x - 2*y(x) + 7)*Derivative(y(x), x) + 4*y(x) - 6,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]