58.7.10 problem 10

Internal problem ID [14665]
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 : Thursday, October 02, 2025 at 09:49:16 AM
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: 0.279 (sec). Leaf size: 738

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

\[ \text {Expression too large to display} \]

✓ Mathematica. Time used: 60.263 (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]
 

Too large to display

✓ Sympy. Time used: 0.886 (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)
 

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