Internal problem ID [7861]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 281.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (y^{2}+2 y x -x^{2}\right ) y^{\prime }-y^{2}+2 y x +x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 53
dsolve((y(x)^2+2*x*y(x)-x^2)*diff(y(x),x)-y(x)^2+2*x*y(x)+x^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {-1+\sqrt {-4 x^{2} c_{1}^{2}+4 c_{1} x +1}}{2 c_{1}} \\ y \relax (x ) = \frac {1+\sqrt {-4 x^{2} c_{1}^{2}+4 c_{1} x +1}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.372 (sec). Leaf size: 75
DSolve[(y[x]^2+2*x*y[x]-x^2)*y'[x]-y[x]^2+2*x*y[x]+x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (e^{c_1}-\sqrt {-4 x^2+4 e^{c_1} x+e^{2 c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {-4 x^2+4 e^{c_1} x+e^{2 c_1}}+e^{c_1}\right ) \\ \end{align*}