72.1.19 problem 22

Internal problem ID [14619]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.2. page 33
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 06:44:45 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.073 (sec). Leaf size: 24

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

\[ y = \frac {-2 \,{\mathrm e}^{4 t} c_{1} -2}{-1+{\mathrm e}^{4 t} c_{1}} \]

✓ Solution by Mathematica

Time used: 0.182 (sec). Leaf size: 42

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

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