29.15.9 problem 417

Internal problem ID [5015]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 417
Date solved : Monday, January 27, 2025 at 10:03:38 AM
CAS classification : [_separable]

\begin{align*} y^{\prime } y+x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(y(x)*diff(y(x),x)+x = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.082 (sec). Leaf size: 39

DSolve[y[x] D[y[x],x]+x==0,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*}