12.7.25 problem 26

Internal problem ID [1735]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page 91
Problem number : 26
Date solved : Saturday, March 29, 2025 at 11:38:03 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} 12 x y+6 y^{3}+\left (9 x^{2}+10 x y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 35

ode:=12*x*y(x)+6*y(x)^3+(9*x^2+10*x*y(x)^2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \ln \left (x \right )-c_1 +\frac {2 \ln \left (\frac {2 y^{2}+3 x}{x}\right )}{11}+\frac {6 \ln \left (\frac {y}{\sqrt {x}}\right )}{11} = 0 \]

✓ Mathematica. Time used: 7.09 (sec). Leaf size: 151

ode=(12*x*y[x]+6*y[x]^3)+(9*x^2+10*x*y[x]^2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \text {Root}\left [2 \text {$\#$1}^5 x^3+3 \text {$\#$1}^3 x^4-c_1\&,1\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^5 x^3+3 \text {$\#$1}^3 x^4-c_1\&,2\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^5 x^3+3 \text {$\#$1}^3 x^4-c_1\&,3\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^5 x^3+3 \text {$\#$1}^3 x^4-c_1\&,4\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^5 x^3+3 \text {$\#$1}^3 x^4-c_1\&,5\right ] \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*x*y(x) + (9*x**2 + 10*x*y(x)**2)*Derivative(y(x), x) + 6*y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - 6*(-2*x - y(x)**2)*y(x)/(x*(9*x + 10*y(x)**2)) cannot be solved by the factorable group method