Internal problem ID [3993]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli
Equations
Problem number: Exercise 11.7, page 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+y-y^{3} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 39
dsolve(diff(y(x),x)+y(x)=x*y(x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {2}{\sqrt {2+4 \,{\mathrm e}^{2 x} c_{1}+4 x}} \\ y \relax (x ) = \frac {2}{\sqrt {2+4 \,{\mathrm e}^{2 x} c_{1}+4 x}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.332 (sec). Leaf size: 50
DSolve[y'[x]+y[x]==x*y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {x+c_1 e^{2 x}+\frac {1}{2}}} \\ y(x)\to \frac {1}{\sqrt {x+c_1 e^{2 x}+\frac {1}{2}}} \\ y(x)\to 0 \\ \end{align*}