Internal problem ID [5046]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 47.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {2 x y^{\prime }+y-y^{2} \sqrt {x -y^{2} x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 38
dsolve(2*x*diff(y(x),x)+y(x)=y(x)^2*sqrt(x-x^2*y(x)^2),y(x), singsol=all)
\[ -\frac {-1+x y \relax (x )^{2}}{y \relax (x ) \sqrt {x -x^{2} y \relax (x )^{2}}}+\frac {\ln \relax (x )}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.836 (sec). Leaf size: 78
DSolve[2*x*y'[x]+y[x]==y[x]^2*Sqrt[x-x^2*y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2}{\sqrt {x \left (\log ^2\left (-\frac {1}{x}\right )+2 c_1 \log \left (-\frac {1}{x}\right )+4+c_1{}^2\right )}} \\ y(x)\to \frac {2}{\sqrt {x \left (\log ^2\left (-\frac {1}{x}\right )+2 c_1 \log \left (-\frac {1}{x}\right )+4+c_1{}^2\right )}} \\ y(x)\to 0 \\ \end{align*}