66.1.2 problem Problem 2

Internal problem ID [13770]
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 2
Date solved : Wednesday, March 05, 2025 at 10:15:15 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 2.104 (sec). Leaf size: 44

ode:=12*x+6*y(x)-9+(5*x+2*y(x)-3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\operatorname {RootOf}\left (128 \textit {\_Z}^{25} c_{1} x^{5}+640 \textit {\_Z}^{20} c_{1} x^{5}+800 \textit {\_Z}^{15} c_{1} x^{5}-1\right )^{5} x -4 x +\frac {3}{2} \]

✓ Mathematica. Time used: 60.061 (sec). Leaf size: 1121

ode=(12*x+6*y[x]-9)+(5*x+2*y[x]-3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 1.114 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*x + (5*x + 2*y(x) - 3)*Derivative(y(x), x) + 6*y(x) - 9,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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