Internal problem ID [8139]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 561.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {f \left (x^{2}+y^{2}\right ) \sqrt {{y^{\prime }}^{2}+1}-y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.454 (sec). Leaf size: 50
dsolve(f(y(x)^2+x^2)*(diff(y(x),x)^2+1)^(1/2)-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x}{\tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\int _{}^{\frac {x^{2} \left (\tan \left (\textit {\_Z} \right )^{2}+1\right )}{\tan \left (\textit {\_Z} \right )^{2}}}\frac {f \left (\textit {\_a} \right )}{\sqrt {-f \left (\textit {\_a} \right )^{2}+\textit {\_a}}\, \textit {\_a}}d \textit {\_a} +2 c_{1} \right )\right )} \]
✓ Solution by Mathematica
Time used: 5.687 (sec). Leaf size: 2138
DSolve[y[x] - x*y'[x] + f[x^2 + y[x]^2]*Sqrt[1 + y'[x]^2]==0,y[x],x,IncludeSingularSolutions -> True]
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