Internal problem ID [12976]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 3. Some basics about First order equations. Additional exercises. page
63
Problem number: 3.4 i.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }+2 y-y^{2}=-2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x)+2*y(x)-y(x)^2=-2,y(x), singsol=all)
\[ y = \frac {\left (\sqrt {3}-3 \tanh \left (\left (x +c_{1} \right ) \sqrt {3}\right )\right ) \sqrt {3}}{3} \]
✓ Solution by Mathematica
Time used: 0.394 (sec). Leaf size: 76
DSolve[y'[x]+2*y[x]-y[x]^2==-2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-\left (\sqrt {3}-1\right ) e^{2 \sqrt {3} (x+c_1)}+1+\sqrt {3}}{1+e^{2 \sqrt {3} (x+c_1)}} y(x)\to 1-\sqrt {3} y(x)\to 1+\sqrt {3} \end{align*}