Internal problem ID [8141]
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]]
Solve \begin {gather*} \boxed {f \left (x^{2}+y^{2}\right ) \sqrt {\left (y^{\prime }\right )^{2}+1}-y^{\prime } x +y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.48 (sec). Leaf size: 84
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)
\begin{align*} y \relax (x ) = \RootOf \left (f \left (\textit {\_Z}^{2}+x^{2}\right ) \sqrt {\frac {\textit {\_Z}^{2}+x^{2}}{\textit {\_Z}^{2}}}\, \textit {\_Z} +x^{2}+\textit {\_Z}^{2}\right ) \\ y \relax (x ) = \frac {x}{\tan \left (\RootOf \left (-2 \textit {\_Z} +\int _{}^{\frac {x^{2} \left (\tan ^{2}\left (\textit {\_Z} \right )+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 )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.992 (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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