Internal problem ID [12299]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y^{2}=-4} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 24
dsolve(diff(y(x),x)=y(x)^2-4,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {2 \left (c_{1} {\mathrm e}^{4 x}+1\right )}{-1+c_{1} {\mathrm e}^{4 x}} \]
✓ Solution by Mathematica
Time used: 1.066 (sec). Leaf size: 40
DSolve[y'[x]==y[x]^2-4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2-2 e^{4 (x+c_1)}}{1+e^{4 (x+c_1)}} y(x)\to -2 y(x)\to 2 \end{align*}