Internal problem ID [3430]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 174.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Bernoulli]
\[ \boxed {x y^{\prime }-\left (1+y x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(x*diff(y(x),x) = (1+x*y(x))*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 x}{-x^{2}+2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.131 (sec). Leaf size: 23
DSolve[x y'[x]==(1+x y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2 x}{x^2-2 c_1} y(x)\to 0 \end{align*}