15.1.11 problem 11

Internal problem ID [2851]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 11
Date solved : Monday, January 27, 2025 at 06:19:56 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 23

dsolve(diff(y(x),x)=x/y(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: 0.081 (sec). Leaf size: 35

DSolve[D[y[x],x]==x/y[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*}