50.8.11 problem 2(c)

Internal problem ID [7927]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Problems for Review and Discovery. Page 53
Problem number : 2(c)
Date solved : Monday, January 27, 2025 at 03:32:42 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (-1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.062 (sec). Leaf size: 15

dsolve([y(x)^2*diff(y(x),x)=x,y(-1) = 3],y(x), singsol=all)
 

\[ y = \frac {\left (12 x^{2}+204\right )^{{1}/{3}}}{2} \]

✓ Solution by Mathematica

Time used: 0.203 (sec). Leaf size: 22

DSolve[{y[x]^2*D[y[x],x]==x,{y[-1]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt [3]{\frac {3}{2}} \sqrt [3]{x^2+17} \]