Internal problem ID [8617]
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]
\[ \boxed {\left (y^{2}+2 y x -x^{2}\right ) y^{\prime }-y^{2}+2 y x=-x^{2}} \]
✓ Solution by Maple
Time used: 0.047 (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 \left (x \right ) = -\frac {-1+\sqrt {-4 c_{1}^{2} x^{2}+4 x c_{1} +1}}{2 c_{1}} y \left (x \right ) = \frac {1+\sqrt {-4 c_{1}^{2} x^{2}+4 x c_{1} +1}}{2 c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 1.669 (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*}