73.7.2 problem 2

Internal problem ID [15160]
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 : 2
Date solved : Tuesday, January 28, 2025 at 07:38:48 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }&=2 y^{2}-6 y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve(x*diff(y(x),x)=2*y(x)^2-6*y(x),y(x), singsol=all)
 

\[ y = \frac {3}{3 c_{1} x^{6}+1} \]

✓ Solution by Mathematica

Time used: 0.241 (sec). Leaf size: 43

DSolve[x*D[y[x],x]==2*y[x]^2-6*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-3) K[1]}dK[1]\&\right ][2 \log (x)+c_1] \\ y(x)\to 0 \\ y(x)\to 3 \\ \end{align*}