73.6.15 problem 7.5 (e)

Internal problem ID [15083]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 7. The exact form and general integrating fators. Additional exercises. page 141
Problem number : 7.5 (e)
Date solved : Monday, March 31, 2025 at 01:22:59 PM
CAS classification : [_separable]

\begin{align*} 3 y+3 y^{2}+\left (2 x +4 x y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.189 (sec). Leaf size: 137

ode:=3*y(x)+3*y(x)^2+(2*x+4*x*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {-c_1 x -\sqrt {c_1^{2} x^{2}-4 \sqrt {c_1 x}}}{2 c_1 x} \\ y &= \frac {-c_1 x +\sqrt {c_1^{2} x^{2}-4 \sqrt {c_1 x}}}{2 c_1 x} \\ y &= \frac {-c_1 x -\sqrt {c_1^{2} x^{2}+4 \sqrt {c_1 x}}}{2 c_1 x} \\ y &= \frac {-c_1 x +\sqrt {c_1^{2} x^{2}+4 \sqrt {c_1 x}}}{2 c_1 x} \\ \end{align*}

✓ Mathematica. Time used: 0.4 (sec). Leaf size: 51

ode=3*y[x]+3*y[x]^2+(2*x+4*x*y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {2 K[1]+1}{K[1] (K[1]+1)}dK[1]\&\right ]\left [-\frac {3 \log (x)}{2}+c_1\right ] \\ y(x)\to -1 \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.673 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((4*x*y(x) + 2*x)*Derivative(y(x), x) + 3*y(x)**2 + 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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