71.3.16 problem 11

Internal problem ID [14366]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 06:27:49 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{2}-3 y \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

dsolve(diff(y(x),x)=y(x)^2-3*y(x),y(x), singsol=all)
 

\[ y = \frac {3}{1+3 \,{\mathrm e}^{3 x} c_{1}} \]

✓ Solution by Mathematica

Time used: 0.224 (sec). Leaf size: 40

DSolve[D[y[x],x]==y[x]^2-3*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 ][x+c_1] \\ y(x)\to 0 \\ y(x)\to 3 \\ \end{align*}