44.4.42 problem 24

Internal problem ID [7055]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 24
Date solved : Monday, January 27, 2025 at 02:42:43 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=10+3 y-y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 24

dsolve(diff(y(x),x)=10+3*y(x)-y(x)^2,y(x), singsol=all)
 

\[ y = \frac {5 \,{\mathrm e}^{7 x} c_{1} +2}{-1+{\mathrm e}^{7 x} c_{1}} \]

✓ Solution by Mathematica

Time used: 0.456 (sec). Leaf size: 48

DSolve[D[y[x],x]==10+3*y[x]-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {5 e^{7 x}+2 e^{7 c_1}}{e^{7 x}-e^{7 c_1}} \\ y(x)\to -2 \\ y(x)\to 5 \\ \end{align*}