Internal problem ID [13355]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }+4 y-y^{3}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(diff(y(x),x)+4*y(x)=y(x)^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {2}{\sqrt {4 \,{\mathrm e}^{8 x} c_{1} +1}} \\ y \left (x \right ) &= \frac {2}{\sqrt {4 \,{\mathrm e}^{8 x} c_{1} +1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.728 (sec). Leaf size: 56
DSolve[y'[x]+4*y[x]==y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2}{\sqrt {1+e^{8 (x+c_1)}}} \\ y(x)\to \frac {2}{\sqrt {1+e^{8 (x+c_1)}}} \\ y(x)\to -2 \\ y(x)\to 0 \\ y(x)\to 2 \\ \end{align*}