Internal problem ID [2936]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 188.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x +y \left (1-x y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 31
dsolve(x*diff(y(x),x)+(1-x*y(x)^2)*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\sqrt {c_{1} x^{2}+2 x}} \\ y \relax (x ) = -\frac {1}{\sqrt {c_{1} x^{2}+2 x}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.329 (sec). Leaf size: 40
DSolve[x y'[x]+(1-x y[x]^2)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {x (2+c_1 x)}} \\ y(x)\to \frac {1}{\sqrt {x (2+c_1 x)}} \\ y(x)\to 0 \\ \end{align*}