47.1.2 problem 2

Internal problem ID [7383]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page 7
Problem number : 2
Date solved : Wednesday, March 05, 2025 at 04:24:41 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 39

ode:=diff(y(x),x) = x^2/y(x)/(x^3+1); 
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: 0.109 (sec). Leaf size: 56

ode=D[y[x],x]==x^2/(y[x]*(1+x^3)); 
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: 0.374 (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)
 

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