Internal problem ID [7999]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 419.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}+2 y y^{\prime }-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.214 (sec). Leaf size: 110
dsolve(x*diff(y(x),x)^2+2*y(x)*diff(y(x),x)-x = 0,y(x), singsol=all)
\begin{align*} x -\frac {\left (-y \relax (x )+\sqrt {x^{2}+y \relax (x )^{2}}\right ) c_{1}}{x \left (\frac {2 x^{2}+6 y \relax (x )^{2}-6 \sqrt {x^{2}+y \relax (x )^{2}}\, y \relax (x )}{x^{2}}\right )^{\frac {2}{3}}} = 0 \\ \frac {c_{1} \left (\sqrt {x^{2}+y \relax (x )^{2}}+y \relax (x )\right )}{x \left (\frac {3 \sqrt {x^{2}+y \relax (x )^{2}}\, y \relax (x )+x^{2}+3 y \relax (x )^{2}}{x^{2}}\right )^{\frac {2}{3}}}+x = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.644 (sec). Leaf size: 6977
DSolve[-x + 2*y[x]*y'[x] + x*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
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