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 : Monday, January 27, 2025 at 02:51:28 PM
CAS classification : [_separable]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x)=x^2/(y(x)*(1+x^3)),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*}

✓ Solution by Mathematica

Time used: 0.109 (sec). Leaf size: 56

DSolve[D[y[x],x]==x^2/(y[x]*(1+x^3)),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*}