64.7.10 problem 10

Internal problem ID [13305]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page 67
Problem number : 10
Date solved : Wednesday, March 05, 2025 at 09:42:32 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 13.538 (sec). Leaf size: 129

ode:=10*x-4*y(x)+12-(x+5*y(x)+3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-3 x -4\right ) {\operatorname {RootOf}\left (-1+\left (243 c_{1} x^{5}+1620 c_{1} x^{4}+4320 c_{1} x^{3}+5760 c_{1} x^{2}+3840 c_{1} x +1024 c_{1} \right ) \textit {\_Z}^{25}+\left (1458 c_{1} x^{5}+9720 c_{1} x^{4}+25920 c_{1} x^{3}+34560 c_{1} x^{2}+23040 c_{1} x +6144 c_{1} \right ) \textit {\_Z}^{20}+\left (2187 c_{1} x^{5}+14580 c_{1} x^{4}+38880 c_{1} x^{3}+51840 c_{1} x^{2}+34560 c_{1} x +9216 c_{1} \right ) \textit {\_Z}^{15}\right )}^{5}}{3}-2 x -3 \]

✓ Mathematica. Time used: 60.315 (sec). Leaf size: 3061

ode=(10*x-4*y[x]+12)-(x+5*y[x]+3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✓ Sympy. Time used: 1.283 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(10*x - (x + 5*y(x) + 3)*Derivative(y(x), x) - 4*y(x) + 12,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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