Internal problem ID [7965]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 385.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-2 y^{\prime } x^{2}+2 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 161
dsolve(diff(y(x),x)^2-2*x^2*diff(y(x),x)+2*x*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x^{4}-\RootOf \left (x^{16}-12 \textit {\_Z}^{2} x^{12}+16 \textit {\_Z}^{3} x^{10}+30 \textit {\_Z}^{4} x^{8}-96 \textit {\_Z}^{5} x^{6}+100 \textit {\_Z}^{6} x^{4}-48 \textit {\_Z}^{7} x^{2}+9 \textit {\_Z}^{8}-16 x^{4} c_{1}\right )^{2}}{2 x} \\ y \relax (x ) = \frac {x^{4}-\RootOf \left (x^{16}-12 \textit {\_Z}^{2} x^{12}-16 \textit {\_Z}^{3} x^{10}+30 \textit {\_Z}^{4} x^{8}+96 \textit {\_Z}^{5} x^{6}+100 \textit {\_Z}^{6} x^{4}+48 \textit {\_Z}^{7} x^{2}+9 \textit {\_Z}^{8}-16 x^{4} c_{1}\right )^{2}}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.451 (sec). Leaf size: 4749
DSolve[2*x*y[x] - 2*x^2*y'[x] + y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
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