Internal problem ID [2572]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 7, page 37
Problem number: 1.b.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-2 y x -2 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve(x^2*diff(y(x),x)-2*x*y(x)-2*y(x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}}{-2 x +c_{1}} \]
✓ Solution by Mathematica
Time used: 0.133 (sec). Leaf size: 22
DSolve[x^2*y'[x]-2*x*y[x]-2*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2}{-2 x+c_1} \\ y(x)\to 0 \\ \end{align*}