Internal problem ID [12307]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {x}{y}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(diff(y(x),x)=x/y(x),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: 0.127 (sec). Leaf size: 35
DSolve[y'[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*}