Internal problem ID [4961]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{2}}{y}=0} \end {gather*}
✓ 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 \relax (x ) = -\frac {\sqrt {6 x^{3}+9 c_{1}}}{3} \\ y \relax (x ) = \frac {\sqrt {6 x^{3}+9 c_{1}}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 50
DSolve[y'[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*}