Internal problem ID [1880]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x}{y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 23
dsolve(diff(y(x),x)=x/y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {x^{2}+c_{1}} \\ y \relax (x ) = -\sqrt {x^{2}+c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.065 (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*}