71.4.3 problem 3

Internal problem ID [14375]
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
Date solved : Tuesday, January 28, 2025 at 06:28:10 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {1}{y x} \end{align*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 25

dsolve(diff(y(x),x)=1/( x*y(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 40

DSolve[D[y[x],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*}