44.5.41 problem 39 (a 3)

Internal problem ID [7103]
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 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 39 (a 3)
Date solved : Tuesday, February 04, 2025 at 12:14:33 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (\frac {1}{4}\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.067 (sec). Leaf size: 25

dsolve([diff(y(x),x)=y(x)^2-4,y(1/4) = 1],y(x), singsol=all)
 

\[ y = \frac {-2 \,{\mathrm e}^{-1+4 x}+6}{3+{\mathrm e}^{-1+4 x}} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 28

DSolve[{D[y[x],x]==y[x]^2-4,{y[1/4]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {6 e-2 e^{4 x}}{e^{4 x}+3 e} \]