71.3.5 problem 3 (E)

Internal problem ID [14355]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 3 (E)
Date solved : Tuesday, January 28, 2025 at 06:27:28 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.065 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.153 (sec). Leaf size: 42

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

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