Internal problem ID [12319]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {1}{y x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(y(x),x)=1/( x*y(x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {2 \ln \left (x \right )+c_{1}} y \left (x \right ) = -\sqrt {2 \ln \left (x \right )+c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.1 (sec). Leaf size: 40
DSolve[y'[x]==1/(x*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2} \sqrt {\log (x)+c_1} y(x)\to \sqrt {2} \sqrt {\log (x)+c_1} \end{align*}