Internal problem ID [8755]
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]
\[ \boxed {x {y^{\prime }}^{2}+2 y y^{\prime }=x} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 111
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 \left (x \right )-\sqrt {y \left (x \right )^{2}+x^{2}}\right ) 2^{\frac {1}{3}} c_{1}}{2 \left (\frac {3 y \left (x \right )^{2}-3 y \left (x \right ) \sqrt {y \left (x \right )^{2}+x^{2}}+x^{2}}{x^{2}}\right )^{\frac {2}{3}} x} &= 0 \\ \frac {c_{1} \left (\sqrt {y \left (x \right )^{2}+x^{2}}+y \left (x \right )\right )}{x {\left (\frac {3 y \left (x \right ) \sqrt {y \left (x \right )^{2}+x^{2}}+x^{2}+3 y \left (x \right )^{2}}{x^{2}}\right )}^{\frac {2}{3}}}+x &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.68 (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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