36.1.38 problem 32

Internal problem ID [6293]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 32
Date solved : Monday, January 27, 2025 at 01:55:09 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {3}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 15

dsolve([diff(y(x),x)=y(x)^2-3*y(x)+2,y(0) = 3/2],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.123 (sec). Leaf size: 18

DSolve[{D[y[x],x]==y[x]^2-3*y[x]+2,{y[0]==3/2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x+2}{e^x+1} \]