Internal problem ID [14228]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-4 y+y^{2}=12} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 24
dsolve(diff(y(t),t)=12+4*y(t)-y(t)^2,y(t), singsol=all)
\[ y \left (t \right ) = \frac {6 c_{1} {\mathrm e}^{8 t}+2}{c_{1} {\mathrm e}^{8 t}-1} \]
✓ Solution by Mathematica
Time used: 0.463 (sec). Leaf size: 47
DSolve[y'[t]==12+4*y[t]-y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {2 \left (3 e^{8 t}+e^{8 c_1}\right )}{e^{8 t}-e^{8 c_1}} \\ y(t)\to -2 \\ y(t)\to 6 \\ \end{align*}