12.9.37 problem 38 part (b)

Internal problem ID [1793]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page 253
Problem number : 38 part (b)
Date solved : Monday, January 27, 2025 at 05:34:56 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+y^{2}-3 y+2&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 20

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

\[ y = \frac {2 \,{\mathrm e}^{x} c_1 -1}{{\mathrm e}^{x} c_1 -1} \]

✓ Solution by Mathematica

Time used: 0.743 (sec). Leaf size: 40

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

\begin{align*} y(x)\to \frac {2 e^x-e^{c_1}}{e^x-e^{c_1}} \\ y(x)\to 1 \\ y(x)\to 2 \\ \end{align*}