29.20.10 problem 555

Internal problem ID [5151]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 555
Date solved : Tuesday, March 04, 2025 at 08:18:54 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.046 (sec). Leaf size: 63

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

\begin{align*} y \left (x \right ) &= \frac {-4 c_{1} x^{2}-\sqrt {-2 c_{1}^{2} x^{4}+6}}{6 c_{1} x} \\ y \left (x \right ) &= \frac {-4 c_{1} x^{2}+\sqrt {-2 c_{1}^{2} x^{4}+6}}{6 c_{1} x} \\ \end{align*}

✓ Mathematica. Time used: 1.705 (sec). Leaf size: 135

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

\begin{align*} y(x)\to -\frac {4 x^2+\sqrt {-2 x^4+6 e^{4 c_1}}}{6 x} \\ y(x)\to \frac {-4 x^2+\sqrt {-2 x^4+6 e^{4 c_1}}}{6 x} \\ y(x)\to -\frac {\sqrt {2} \sqrt {-x^4}+4 x^2}{6 x} \\ y(x)\to \frac {\sqrt {2} \sqrt {-x^4}-4 x^2}{6 x} \\ \end{align*}

✓ Sympy. Time used: 1.689 (sec). Leaf size: 42

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

\[ \left [ y{\left (x \right )} = - \frac {2 x}{3} - \frac {\sqrt {C_{1} - 2 x^{4}}}{6 x}, \ y{\left (x \right )} = - \frac {2 x}{3} + \frac {\sqrt {C_{1} - 2 x^{4}}}{6 x}\right ] \]