73.3.46 problem 4.8 (e)

Internal problem ID [15080]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.8 (e)
Date solved : Tuesday, January 28, 2025 at 07:29:59 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 11

dsolve([x*diff(y(x),x)=y(x)^2-y(x),y(1) = 2],y(x), singsol=all)
 

\[ y = -\frac {2}{x -2} \]

✓ Solution by Mathematica

Time used: 0.277 (sec). Leaf size: 12

DSolve[{x*D[y[x],x]==y[x]^2-y[x],{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {2}{x-2} \]