Internal problem ID [7919]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 339.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x \sqrt {1+x^{2}+y^{2}}-y \left (x^{2}+y^{2}\right )\right ) y^{\prime }-x \left (x^{2}+y^{2}\right )-y \sqrt {1+x^{2}+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 27
dsolve((x*(x^2+y(x)^2+1)^(1/2)-y(x)*(y(x)^2+x^2))*diff(y(x),x)-y(x)*(x^2+y(x)^2+1)^(1/2)-x*(y(x)^2+x^2) = 0,y(x), singsol=all)
\[ \arctan \left (\frac {y \relax (x )}{x}\right )-\sqrt {1+x^{2}+y \relax (x )^{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.264 (sec). Leaf size: 27
DSolve[-(x*(x^2 + y[x]^2)) - y[x]*Sqrt[1 + x^2 + y[x]^2] + (-(y[x]*(x^2 + y[x]^2)) + x*Sqrt[1 + x^2 + y[x]^2])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {ArcTan}\left (\frac {x}{y(x)}\right )+\sqrt {x^2+y(x)^2+1}=c_1,y(x)\right ] \]