Internal problem ID [13384]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }+3 y-3 y^{3}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(diff(y(x),x)+3*y(x)=3*y(x)^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {1}{\sqrt {{\mathrm e}^{6 x} c_{1} +1}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {{\mathrm e}^{6 x} c_{1} +1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.675 (sec). Leaf size: 58
DSolve[y'[x]+3*y[x]==3*y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {1+e^{6 x+2 c_1}}} \\ y(x)\to \frac {1}{\sqrt {1+e^{6 x+2 c_1}}} \\ y(x)\to -1 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}