73.6.6 problem 7.4 (d)

Internal problem ID [15066]
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 : 7.4 (d)
Date solved : Thursday, March 13, 2025 at 05:34:44 AM
CAS classification : [_exact, _rational, _Bernoulli]

\begin{align*} 1+3 x^{2} y^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 50

ode:=1+3*x^2*y(x)^2+(2*x^3*y(x)+6*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {\sqrt {\left (x^{3}+3\right ) \left (-x +c_{1} \right )}}{x^{3}+3} \\ y &= -\frac {\sqrt {\left (x^{3}+3\right ) \left (-x +c_{1} \right )}}{x^{3}+3} \\ \end{align*}

✓ Mathematica. Time used: 0.235 (sec). Leaf size: 50

ode=1+3*x^2*y[x]^2+(2*x^3*y[x]+6*y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {\sqrt {-x+c_1}}{\sqrt {x^3+3}} \\ y(x)\to \frac {\sqrt {-x+c_1}}{\sqrt {x^3+3}} \\ \end{align*}

✓ Sympy. Time used: 0.620 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**2*y(x)**2 + (2*x**3*y(x) + 6*y(x))*Derivative(y(x), x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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