66.1.35 problem Problem 49

Internal problem ID [13811]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 49
Date solved : Monday, March 31, 2025 at 08:13:38 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {3 x -4 y-2}{3 x -4 y-3} \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 19

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

\[ y = \frac {3 x}{4}+\operatorname {LambertW}\left (\frac {c_1 \,{\mathrm e}^{-\frac {1}{4}+\frac {x}{4}}}{4}\right )+\frac {1}{4} \]

✓ Mathematica. Time used: 1.006 (sec). Leaf size: 41

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

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

✓ Sympy. Time used: 2.788 (sec). Leaf size: 116

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

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