Internal problem ID [8023]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 443.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {x \left (x y^{\prime }-y\right )^{2}-y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 5.093 (sec). Leaf size: 221
dsolve(x*(x*diff(y(x),x)-y(x))^2-diff(y(x),x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {2}{9 x^{2}} \\ y \relax (x ) = \frac {\left (\RootOf \left (-729 x^{12}+\textit {\_Z}^{8} c_{1}+4 \textit {\_Z}^{7} c_{1}+4 \textit {\_Z}^{6} c_{1}-4 \textit {\_Z}^{5} c_{1}-10 \textit {\_Z}^{4} c_{1}-4 \textit {\_Z}^{3} c_{1}+4 \textit {\_Z}^{2} c_{1}+4 \textit {\_Z} c_{1}+c_{1}\right )-2\right ) \left (\RootOf \left (-729 x^{12}+\textit {\_Z}^{8} c_{1}+4 \textit {\_Z}^{7} c_{1}+4 \textit {\_Z}^{6} c_{1}-4 \textit {\_Z}^{5} c_{1}-10 \textit {\_Z}^{4} c_{1}-4 \textit {\_Z}^{3} c_{1}+4 \textit {\_Z}^{2} c_{1}+4 \textit {\_Z} c_{1}+c_{1}\right )+1\right )}{9 x^{2}} \\ y \relax (x ) = \frac {\left (\RootOf \left (-729 c_{1} x^{12}+\textit {\_Z}^{8}-12 \textit {\_Z}^{7}+60 \textit {\_Z}^{6}-160 \textit {\_Z}^{5}+240 \textit {\_Z}^{4}-192 \textit {\_Z}^{3}+64 \textit {\_Z}^{2}\right )-2\right ) \left (\RootOf \left (-729 c_{1} x^{12}+\textit {\_Z}^{8}-12 \textit {\_Z}^{7}+60 \textit {\_Z}^{6}-160 \textit {\_Z}^{5}+240 \textit {\_Z}^{4}-192 \textit {\_Z}^{3}+64 \textit {\_Z}^{2}\right )+1\right )}{9 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.199 (sec). Leaf size: 2353
DSolve[-y'[x] + x*(-y[x] + x*y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
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