Internal problem ID [7643]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 62.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y-x^{2} \sqrt {x^{2}-y^{2}}}{x y \sqrt {x^{2}-y^{2}}+x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 34
dsolve(diff(y(x),x) - (y(x)-x^2*sqrt(x^2-y(x)^2))/(x*y(x)*sqrt(x^2-y(x)^2)+x)=0,y(x), singsol=all)
\[ \frac {y \relax (x )^{2}}{2}+\arctan \left (\frac {y \relax (x )}{\sqrt {x^{2}-y \relax (x )^{2}}}\right )+\frac {x^{2}}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 3.063 (sec). Leaf size: 44
DSolve[y'[x] - (y[x]-x^2*Sqrt[x^2-y[x]^2])/(x*y[x]*Sqrt[x^2-y[x]^2]+x)==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\text {ArcTan}\left (\frac {\sqrt {x^2-y(x)^2}}{y(x)}\right )+\frac {x^2}{2}+\frac {y(x)^2}{2}=c_1,y(x)\right ] \]