Internal problem ID [4441]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2}+3 y-2=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = {\frac {3}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.081 (sec). Leaf size: 15
dsolve([diff(y(x),x)=y(x)^2-3*y(x)+2,y(0) = 3/2],y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{x}+2}{{\mathrm e}^{x}+1} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 14
DSolve[{y'[x]==y[x]^2-3*y[x]+2,{y[0]==3/2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{e^x+1}+1 \\ \end{align*}