10.2.2 problem 2

Internal problem ID [1130]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 2
Date solved : Saturday, March 29, 2025 at 10:40:44 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 39

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

\begin{align*} y &= -\frac {\sqrt {6 \ln \left (x^{3}+1\right )+9 c_1}}{3} \\ y &= \frac {\sqrt {6 \ln \left (x^{3}+1\right )+9 c_1}}{3} \\ \end{align*}

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 56

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

\begin{align*} y(x)\to -\sqrt {\frac {2}{3}} \sqrt {\log \left (x^3+1\right )+3 c_1} \\ y(x)\to \sqrt {\frac {2}{3}} \sqrt {\log \left (x^3+1\right )+3 c_1} \\ \end{align*}

✓ Sympy. Time used: 0.324 (sec). Leaf size: 36

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

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