73.5.9 problem 6.5 (a)

Internal problem ID [15120]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.5 (a)
Date solved : Tuesday, January 28, 2025 at 07:33:49 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

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

\begin{align*} y &= \frac {1}{\sqrt {{\mathrm e}^{6 x} c_{1} +1}} \\ y &= -\frac {1}{\sqrt {{\mathrm e}^{6 x} c_{1} +1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.197 (sec). Leaf size: 53

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) K[1] (K[1]+1)}dK[1]\&\right ][3 x+c_1] \\ y(x)\to -1 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}