Internal problem ID [3877]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 3
Problem number: 8.1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _exact]
Solve \begin {gather*} \boxed {\frac {x}{\sqrt {1+x^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {1+x^{2}+y^{2}}}+\frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.234 (sec). Leaf size: 27
dsolve( x/sqrt(1+x^2+y(x)^2) + y(x)/sqrt(1+x^2+y(x)^2)*diff(y(x),x)+ y(x)/(x^2+y(x)^2) - x/(x^2+y(x)^2)*diff(y(x),x)=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: 0.261 (sec). Leaf size: 27
DSolve[ x/Sqrt[1+x^2+y[x]^2] + y[x]/Sqrt[1+x^2+y[x]^2]*y'[x]+y[x]/(x^2+y[x]^2) - x/(x^2+y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {ArcTan}\left (\frac {x}{y(x)}\right )+\sqrt {x^2+y(x)^2+1}=c_1,y(x)\right ] \]