60.1.558 problem 561

Internal problem ID [10572]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 561
Date solved : Monday, January 27, 2025 at 09:08:32 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} f \left (x^{2}+y^{2}\right ) \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.671 (sec). Leaf size: 42

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)
 

\[ y = \cot \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\int _{}^{\csc \left (\textit {\_Z} \right )^{2} x^{2}}\frac {f \left (\textit {\_a} \right )}{\sqrt {-f \left (\textit {\_a} \right )^{2}+\textit {\_a}}\, \textit {\_a}}d \textit {\_a} +2 c_{1} \right )\right ) x \]

✓ Solution by Mathematica

Time used: 2.706 (sec). Leaf size: 2138

DSolve[y[x] - x*D[y[x],x] + f[x^2 + y[x]^2]*Sqrt[1 + D[y[x],x]^2]==0,y[x],x,IncludeSingularSolutions -> True]
 

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