Internal problem ID [10146]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 16. Integrating
factors by inspection. Page 23
Problem number: Ex 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x -y^{2}+2 y x y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve((x-y(x)^2)+2*x*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {-x \ln \relax (x )+x c_{1}} \\ y \relax (x ) = -\sqrt {-x \ln \relax (x )+x c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.189 (sec). Leaf size: 44
DSolve[(x-y[x]^2)+2*x*y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x} \sqrt {-\log (x)+c_1} \\ y(x)\to \sqrt {x} \sqrt {-\log (x)+c_1} \\ \end{align*}