74.4.70 problem 67

Internal problem ID [15963]
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 : 67
Date solved : Tuesday, January 28, 2025 at 08:24:55 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=12+4 y-y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.070 (sec). Leaf size: 24

dsolve(diff(y(t),t)=12+4*y(t)-y(t)^2,y(t), singsol=all)
 

\[ y = \frac {6 \,{\mathrm e}^{8 t} c_{1} +2}{{\mathrm e}^{8 t} c_{1} -1} \]

✓ Solution by Mathematica

Time used: 0.215 (sec). Leaf size: 44

DSolve[D[y[t],t]==12+4*y[t]-y[t]^2,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-6) (K[1]+2)}dK[1]\&\right ][-t+c_1] \\ y(t)\to -2 \\ y(t)\to 6 \\ \end{align*}