49.21.2 problem 1(b)

Internal problem ID [7732]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 190
Problem number : 1(b)
Date solved : Monday, January 27, 2025 at 03:10:53 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(y(x)*diff(y(x),x)=x,y(x), singsol=all)
 

\begin{align*} y &= \sqrt {x^{2}+c_{1}} \\ y &= -\sqrt {x^{2}+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.082 (sec). Leaf size: 35

DSolve[y[x]*D[y[x],x]==x,y[x],x,IncludeSingularSolutions -> True]
 

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