74.4.32 problem 32

Internal problem ID [15925]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 32
Date solved : Tuesday, January 28, 2025 at 08:22:55 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.072 (sec). Leaf size: 19

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

\[ y = \frac {-2+{\mathrm e}^{x} c_{1}}{-1+{\mathrm e}^{x} c_{1}} \]

✓ Solution by Mathematica

Time used: 0.222 (sec). Leaf size: 42

DSolve[D[y[x],x]==y[x]^2-3*y[x]+2,y[x],x,IncludeSingularSolutions -> True]
 

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