73.4.9 problem 5.1 (i)

Internal problem ID [15091]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.1 (i)
Date solved : Tuesday, January 28, 2025 at 07:30:24 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+4 y&=y^{3} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(y(x),x)+4*y(x)=y(x)^3,y(x), singsol=all)
 

\begin{align*} y &= -\frac {2}{\sqrt {4 \,{\mathrm e}^{8 x} c_{1} +1}} \\ y &= \frac {2}{\sqrt {4 \,{\mathrm e}^{8 x} c_{1} +1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.220 (sec). Leaf size: 51

DSolve[D[y[x],x]+4*y[x]==y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-2) K[1] (K[1]+2)}dK[1]\&\right ][x+c_1] \\ y(x)\to -2 \\ y(x)\to 0 \\ y(x)\to 2 \\ \end{align*}