Internal problem ID [2925]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 177.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x -y \left (2 y x +1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 15
dsolve(x*diff(y(x),x) = y(x)*(1+2*x*y(x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {x}{-x^{2}+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.136 (sec). Leaf size: 22
DSolve[x y'[x]==y[x](1+2 x y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{-x^2+c_1} \\ y(x)\to 0 \\ \end{align*}