Internal problem ID [2838]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 83.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+y \left (1-x y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 39
dsolve(diff(y(x),x)+y(x)*(1-x*y(x)^2) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {2}{\sqrt {2+4 c_{1} {\mathrm e}^{2 x}+4 x}} \\ y \relax (x ) = \frac {2}{\sqrt {2+4 c_{1} {\mathrm e}^{2 x}+4 x}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.31 (sec). Leaf size: 50
DSolve[y'[x]+y[x](1-x y[x]^2)==0,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*}