Internal problem ID [3471]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 734.
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: 0.06 (sec). Leaf size: 27
dsolve((x*sqrt(1+x^2+y(x)^2)-y(x)*(x^2+y(x)^2))*diff(y(x),x) = x*(x^2+y(x)^2)+y(x)*sqrt(1+x^2+y(x)^2),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: 0.267 (sec). Leaf size: 27
DSolve[(x Sqrt[1+x^2+y[x]^2]-y[x] (x^2+y[x]^2))y'[x]==x(x^2+y[x]^2)+y[x]Sqrt[1+x^2+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {ArcTan}\left (\frac {x}{y(x)}\right )+\sqrt {x^2+y(x)^2+1}=c_1,y(x)\right ] \]