47.1.1 problem 1

Internal problem ID [7382]
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 : 1
Date solved : Monday, January 27, 2025 at 02:51:25 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {x^{2}}{y} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(y(x),x)=x^2/y(x),y(x), singsol=all)
 

\begin{align*} y &= -\frac {\sqrt {6 x^{3}+9 c_{1}}}{3} \\ y &= \frac {\sqrt {6 x^{3}+9 c_{1}}}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.094 (sec). Leaf size: 50

DSolve[D[y[x],x]==x^2/y[x],y[x],x,IncludeSingularSolutions -> True]
 

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