10.2.1 problem 1

Internal problem ID [1129]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 1
Date solved : Monday, January 27, 2025 at 04:35:02 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (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: 0.084 (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*}