Internal problem ID [9300]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1726 (book 6.135).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]
\[ \boxed {y^{\prime \prime } \left (x -y\right )-\left (y^{\prime }+1\right ) \left ({y^{\prime }}^{2}+1\right )=0} \]
✓ Solution by Maple
Time used: 0.187 (sec). Leaf size: 106
dsolve(diff(diff(y(x),x),x)*(x-y(x))-(diff(y(x),x)+1)*(diff(y(x),x)^2+1)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = x +\operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}-\frac {c_{1}^{2} \textit {\_f}^{2}-1}{c_{1}^{2} \textit {\_f}^{2}+c_{1} \sqrt {-c_{1}^{2} \textit {\_f}^{2}+2}\, \textit {\_f} -2}d \textit {\_f} +c_{2} \right ) \\ y \left (x \right ) = x +\operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}-\frac {c_{1}^{2} \textit {\_f}^{2}-1}{-2+c_{1}^{2} \textit {\_f}^{2}-c_{1} \sqrt {-c_{1}^{2} \textit {\_f}^{2}+2}\, \textit {\_f}}d \textit {\_f} +c_{2} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 29.195 (sec). Leaf size: 18840
DSolve[(-1 - y'[x])*(1 + y'[x]^2) + (x - y[x])*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
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