73.2.9 problem 3.4 i

Internal problem ID [15032]
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
Date solved : Tuesday, January 28, 2025 at 07:28:04 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

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

\[ y = 1-\sqrt {3}\, \tanh \left (\left (x +c_{1} \right ) \sqrt {3}\right ) \]

✓ Solution by Mathematica

Time used: 0.182 (sec). Leaf size: 55

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2-2 K[1]-2}dK[1]\&\right ][x+c_1] \\ y(x)\to 1-\sqrt {3} \\ y(x)\to 1+\sqrt {3} \\ \end{align*}