73.7.17 problem 17

Internal problem ID [15175]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 07:40:04 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {1}{y x -3 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 35

dsolve(diff(y(x),x)=1/(x*y(x)-3*x),y(x), singsol=all)
 

\begin{align*} y &= 3-\sqrt {9+2 \ln \left (x \right )+2 c_{1}} \\ y &= 3+\sqrt {9+2 \ln \left (x \right )+2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.101 (sec). Leaf size: 43

DSolve[D[y[x],x]==1/(x*y[x]-3*x),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 3-\sqrt {2 \log (x)+9+2 c_1} \\ y(x)\to 3+\sqrt {2 \log (x)+9+2 c_1} \\ \end{align*}